# Help solving: Adding a few equations to ODE slows JuMP \>100x

**URL:** <https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump\
**Created:** [March 7, 2024, 8:14pm UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321 "2024-03-07T20:14:51Z")\
**Posts on this page:** 19\
**Page:** 1

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 7, 2024, 8:14pm UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/1 "2024-03-07T20:14:51Z")

</div>

I’m using JuMP with Ipopt and AppleAccelerate.jl

Following the rocket control tutorial, I coded a simplified set of differential equations where I optimize a control function. My simplified code takes \<2s to run:

```julia
	# dynamical variables
	u = @JuMP.variables(model,begin
		0 <= φ_R[1:n] <= 0.45
		0 <= c_pc[1:n]
		0 <= M[1:n]
	end);

	# optimization knob
	@variable(model, 0 <= α_R[1:n] <= 0.45 )

	# helper functions
	@expression(model, γ[j = 1:n], 10 * c_pc[j]/(c_pc[j] + 0.03))
	@expression(model, λ[j = 1:n], γ[j] * φ_R[j])

	du = Vector{Vector{NonlinearExpr}}(undef, length(u))
	# growth dynamics
	du[1] = @expression(model, δφ_R[j = 1:n], (α_R[j] - φ_R[j]) * λ[j])
	du[2] = @expression(model, δc_pc[j =1:n], νmax*(0.45 - φ_R[j]) - (1 + c_pc[j]) * λ[j] )
	du[3] = @expression(model, δM[j = 1:n], M[j] * λ[j])

```

(and with trapezoidal integration)

the expanded model takes ~250s to run:

```julia
	# dynamical variables
	u = @JuMP.variables(model,begin
		0 <= φ_R[1:n] <= 0.45
		0 <= c_pc[1:n]
		0 <= C_bnd[1:n]
		0 <= C_in[1:n]
		0 <= M[1:n]
	end);

	# optimization knob
	@variable(model, 0 <= α_R[1:n] <= 0.45 )

	# helper functions
	C_max = 1e-5
	@expression(model, C_out[j = 1:n], C_max)
	@expression(model, C_Rf[j = 1:n], φ_R[j] * 6.4e-5 - C_bnd[j])
	@expression(model, φ_Rf[j = 1:n], φ_R[j] - C_bnd[j] / 6.4e-5)
	@expression(model, φ_M[j = 1:n], 0.45 - φ_R[j])
	@expression(model, γ[j = 1:n], 10 * c_pc[j]/(c_pc[j] + 0.03))
	@expression(model, λ[j = 1:n], γ[j] * φ_Rf[j])

	du = Vector{Vector{NonlinearExpr}}(undef, length(u))
	# growth dynamics
	k_on = 1.1 # 4e5
	du[1] = @expression(model, δφ_R[j = 1:n], (α_R[j] - φ_R[j]) * λ[j])
	du[2] = @expression(model, δc_pc[j =1:n], 5*(0.45 - φ_R[j]) - (1 + c_pc[j]) * λ[j] )
	du[3] = @expression(model, δC_bnd[j = 1:n], k_on*C_in[j]*C_Rf[j] - 0.4*C_bnd[j] - λ[j]*C_bnd[j])
	du[4] = @expression(model, δC_in[j = 1:n], 
		1.5*(C_out[j] - C_in[j]) + 0.4*C_bnd[j] - k_on*C_Rf[j]*C_in[j] - λ[j]*C_in[j]
	)
	du[5] = @expression(model, δM[j = 1:n], M[j] * λ[j])

```

There is an even more expanded model with another two equations that I haven’t been patient enough to get to converge at all. I previously solved these equations in the DifferentialEquations package, so barring typos, I’m reasonably confident that the equations are not the problem.

Any suggestions on how to speed up finding the optimal control law would be much appreciated!

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 7, 2024, 8:45pm UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/2 "2024-03-07T20:45:03Z")

</div>

Can you provide a reproducible example?

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 2:44am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/3 "2024-03-08T02:44:21Z")

</div>

The actual numerics functions

```julia
begin
	abstract type AbstractIntegrationRule end
	struct TrapezoidalIntegrationRule <: AbstractIntegrationRule end
	
	struct JumpConfig{T<:AbstractIntegrationRule}
		n::Int # mesh points
		Δt::Float64 # time step
		integration_rule::T
	end
	
	function integration_JuMP!(model, u, du, jc, ::TrapezoidalIntegrationRule)
		@variable(model, δt[1:jc.n] == jc.Δt)
	
		for t in 2:jc.n
			s = t - 1
			for k in 1:length(u)
				@constraint(model, u[k][t] == u[k][s] + 0.5 * δt[t] * (du[k][s] + du[k][t]))
			end
		end
	end
	
	function fast_sim(
		u0, jc::JumpConfig
	)
		n = jc.n
		model = Model(Ipopt.Optimizer)
	
		# dynamical variables
		u = @JuMP.variables(model,begin
			0 <= φ_R[1:n] <= 0.45
			0 <= c_pc[1:n]
			0 <= M[1:n]
		end);
	
		# optimization knob
		@variable(model, 0 <= α_R[1:n] <= 0.45 )
	
		# helper functions
		@expression(model, γ[j = 1:n], 10 * c_pc[j]/(c_pc[j] + 0.03))
		@expression(model, λ[j = 1:n], γ[j] * φ_R[j])
	
		du = Vector{Vector{NonlinearExpr}}(undef, length(u))
		# growth dynamics
		du[1] = @expression(model, δφ_R[j = 1:n], (α_R[j] - φ_R[j]) * λ[j])
		du[2] = @expression(model, δc_pc[j =1:n], 5*(0.45 - φ_R[j]) - (1 + c_pc[j]) * λ[j] )
		du[3] = @expression(model, δM[j = 1:n], M[j] * λ[j])
	
		# integration
		integration_JuMP!(model, u, du, jc, TrapezoidalIntegrationRule())
	
		@objective(model, Max, M[n])
		set_silent(model)
	
		# one set of initial conditions
		for i in 1:length(u)
			fix(u[i][1], u0[i]; force = true)
		end
	
		optimize!(model)
		Ls = value.(λ)
		Rs = value.(φ_R)
		aRs = value.(α_R)
		cpcs = value.(c_pc)
	
		return Rs, cpcs, aRs, Ls
	end
	
	function slow_sim(
		u0, jc::JumpConfig; Kd = 1e-6, k_on = 4e6, C_max = 1e-6
	)
		n = jc.n
		model = Model(Ipopt.Optimizer)
	
		# dynamical variables
		u = @JuMP.variables(model,begin
			0 <= φ_R[1:n] <= 0.45
			0 <= c_pc[1:n]
			0 <= C_bnd[1:n]
			0 <= C_in[1:n]
			0 <= M[1:n]
		end);
	
		# optimization knob
		@variable(model, 0 <= α_R[1:n] <= 0.45 )
	
		# helper functions
		@expression(model, C_out[j = 1:n], C_max)
		@expression(model, C_Rf[j = 1:n], φ_R[j] * 6.4e-5 - C_bnd[j])
		
		@expression(model, φ_Rf[j = 1:n], φ_R[j] - C_bnd[j] / 6.4e-5)
		@constraint(model, φ_Rf .>= 0)
	
		@expression(model, φ_M[j = 1:n], 0.45 - φ_R[j])
		@expression(model, γ[j = 1:n], 10 * c_pc[j]/(c_pc[j] + 0.03))
		@expression(model, λ[j = 1:n], γ[j] * φ_Rf[j])
	
	
		du = Vector{Vector{NonlinearExpr}}(undef, length(u))
		# growth dynamics
		k_off = k_on * Kd # 0.4 # 40
		du[1] = @expression(model, δφ_R[j = 1:n], (α_R[j] - φ_R[j]) * λ[j])
		# 1/s in mass fractions -> multiply by ρ to get conc.
		du[2] = @expression(model, δc_pc[j =1:n], 5*(0.45 - φ_R[j]) - (1 + c_pc[j]) * λ[j] )
		du[3] = @expression(model, δC_bnd[j = 1:n], k_on*C_in[j]*C_Rf[j] - k_off*C_bnd[j] - λ[j]*C_bnd[j])
		du[4] = @expression(model, δC_in[j = 1:n], 
			1.5*(C_out[j] - C_in[j]) + k_off*C_bnd[j] - k_on*C_Rf[j]*C_in[j] - λ[j]*C_in[j]
		)
		du[5] = @expression(model, δM[j = 1:n], M[j] * λ[j])
	
		# integration
		integration_JuMP!(model, u, du, jc, TrapezoidalIntegrationRule())
	
		@objective(model, Max, M[n])
		set_silent(model)
	
		for i in 1:length(u)
			fix(u[i][1], u0[i]; force = true)
		end
	
		optimize!(model)
		Ls = value.(λ)
		Rs = value.(φ_R)
		a_Rs = value.(α_R)
		cpcs = value.(c_pc)
		C_bnds = value.(C_bnd)
		C_ins = value.(C_in)
	
		return Rs, a_Rs, cpcs, C_bnds, C_ins, Ls
	end
end

```

Example code to run it:

```julia
begin
       u0_fast = [0.1, 0.05, 0.001]

        steps = 1000
	δt = 1/250
	jc = JumpConfig(steps, δt, TrapezoidalIntegrationRule())
	fast_soln = fast_sim(u0_fast, jc)
end

```

It takes ~2s to run the above in a Pluto NB ^

```julia
u0_slow = [0.1, 0.05, 0.0, 0.0, 0.001]
slow_soln = slow_sim(u0_slow, jc)

```

and ~30s to run ^ the slow sim.

I was able to speed it up by adding a constraint, \lambda \geq 0, but still looking for it to be faster.

The speed is significantly affected by the magnitudes of `k_on` and `C_max`; I have them set lower than I want them to get the simulation to run. Something about the significant difference in the parameter magnitudes is significantly slowing down the optimization.

Here are also some plotting utilities for plotting the slow solution, in case it is useful. The results from the above optimizations can be plotted like `plot_soln(slow_soln, jc)`.

My goal is to figure out how to get the `slow_sim` faster, `fast_sim` was just an intermediate step that I am sharing for background.

```julia
const green = colorant"#04C13C"
const purp = colorant"#BA79BE"
const pink = colorant"#FA007B"
const blue = colorant"#05A8C9"
const brown = colorant"#8B4513"
const orange = colorant"#FFA500"

const thick_line = 3.5
const thin_line = 2
const extra_thin_line = 1
const opt_color = :gray

function plot_soln(soln, jc::JumpConfig)
    Rs = soln[1]
    aRs = soln[2]
    cpcs = soln[3]
    normed_cpcs = cpcs ./ 0.03
    C_bnds = soln[4]
    C_ins = soln[5]
    Ls = soln[6]

    ts = cumsum([0; repeat([jc.Δt], jc.n)])[1:end-1]

    plt_growth = λ_plot(ts, Ls)
    plt_pfractions = φR_plot(ts, Rs, aRs)
    plt_pcursors = precursor_plot(ts, normed_cpcs, xlab=true)
    plt_ABX = ABX_plot(ts, C_ins, C_bnds, xlab=true)

    p = plot(
        plt_pfractions, plt_growth, plt_pcursors, plt_ABX;
        layout = grid(2,2), size = (700,700), legend=:right
    )
    return p
end

function precursor_plot(ts, normed_c_pcs; subset_idxs=nothing, xlab=false)
    if xlab
        xlab = "Time (hrs)"
    else
        xlab = ""
    end
    plt = plot_series(
        ts, normed_c_pcs, blue;
        title = "Precursors",
        xlab = xlab,
        ylab = "Concentration (Km)",
        subset_idxs = subset_idxs,
    )
    return plt
end

function φR_plot(ts, φ_Rs, α_Rs; subset_idxs=nothing, xlab=false)
    if xlab
        xlab = "Time (hrs)"
    else
        xlab = ""
    end
    plt = plot_series(
        ts, φ_Rs, purp;
        title = "Protein Fractions",
        xlab = xlab,
        ylab = "Mass Fraction",
        subset_idxs = subset_idxs,
    )
    plot_series!(
        plt, ts, α_Rs, pink;
        subset_idxs = subset_idxs, lw = extra_thin_line, ls = :dashdot,
    )
    return plt
end

function λ_plot(ts, λs; subset_idxs=nothing, xlab=false)
    if xlab
        xlab = "Time (hrs)"
    else
        xlab = ""
    end
    plt = plot_series(
        ts, λs, green;
        title = "Growth Rate",
        xlab = xlab,
        ylab = "Rate (1/hr)",
        subset_idxs = subset_idxs,
    )
    return plt
end

function ABX_plot(ts, C_ins, C_bnds; subset_idxs=nothing, xlab=false)
    if xlab
        xlab = "Time (hrs)"
    else
        xlab = ""
    end
    plt = plot_series(
        ts, C_bnds, orange;
        title = "ABX",
        xlab = xlab,
        ylab = "Concentration ([M])",
        subset_idxs = subset_idxs,
        label = "Bound to Ribosome"
    )
    plot_series!(
        plt, ts, C_ins, brown;
        subset_idxs = subset_idxs,
        label = "Intracellular",
    )

    return plt
end

function plot_series(
    ts, xs, color::RGB;
    title, xlab, ylab,
    subset_idxs=nothing, lw = thick_line,
    ls = :solid, label = nothing
)
    xs, n_plots = subset_series(xs, subset_idxs)
    colors = set_colors(n_plots, color)

    plt = plot(title = title, xlabel = xlab, ylabel = ylab)
    for i in 1:n_plots
        if i == n_plots
            lab = label
        else
            lab = nothing
        end
        plot!(
            ts,
            xs[:,i];
            label = lab,
            linecolor = colors[i],
            linewidth = lw, linestyle = ls,
        )
    end
    return plt
end

function plot_series!(
    plt, ts, xs, color::RGB;
    subset_idxs=nothing, lw = thick_line,
    ls = :solid, label = nothing
)
    xs, n_plots = subset_series(xs, subset_idxs)
    colors = set_colors(n_plots, color)

    for i in 1:n_plots
        if i == n_plots
            lab = label
        else
            lab = nothing
        end
        plot!(
            plt,
            ts,
            xs[:,i];
            label = lab,
            linecolor = colors[i],
            linewidth = lw, linestyle = ls,
        )
    end
    return plt
end

function set_colors(n_plots, base)
    if n_plots == 1
        return [base]
    else
        return gen_color_range(n_plots, base)
    end
end

function subset_series(series, subset_idxs)
    if series isa Matrix
        if subset_idxs != nothing
            series = series[:, subset_idxs]
        end
        n_plots = size(series)[2]
    elseif series isa Vector
        n_plots = 1
    else
        error("series must be a matrix or vector")
    end
    return series, n_plots
end

function gen_color_range(n, end_color, start_color=colorant"cornsilk3")
	if n == 1
		return [end_color]
	end
	# rescale 
	xs = (0:n-1)/(5/4*(n-1)) .+ 0.2
	cs = ColorScheme(range(start_color, end_color))
	return get(cs, xs)
end

```

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 8, 2024, 2:52am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/4 "2024-03-08T02:52:52Z")

</div>

Can you provide the inputs for `fast_sim` and `slow_sim`?

Have you looked at the Ipopt logs? What part is taking the time?

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 2:57am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/5 "2024-03-08T02:57:33Z")

</div>

how do I look at the Ipopt logs?

my intution is that it’s taking a long time due to the fact that the added DEs have terms that have very large and very small magnitudes, that also feedback onto the rest of the dynamics

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 8, 2024, 2:58am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/6 "2024-03-08T02:58:21Z")

</div>

> how do I look at the Ipopt logs?

Comment out `set_silent(model)`

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 8, 2024, 3:00am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/7 "2024-03-08T03:00:09Z")

</div>

I get `ERROR: LoadError: UndefVarError: `νmax` not defined`.

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 3:02am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/8 "2024-03-08T03:02:34Z")

</div>

I fixed it in the above code, but you can replace it with a `5`. I originally was passing in a struct but removed it to minimize extra code

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 3:04am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/9 "2024-03-08T03:04:51Z")

</div>

The Ipopt log gives me:

(I cut out some lines in the middle of the objective changing bc it exceeded the max character count)

```julia
This is Ipopt version 3.14.14, running with linear solver MUMPS 5.6.2.

Number of nonzeros in equality constraint Jacobian...: 37944
Number of nonzeros in inequality constraint Jacobian.: 1998
Number of nonzeros in Lagrangian Hessian.............: 164721

Total number of variables............................: 5995
                     variables with only lower bounds: 3996
                variables with lower and upper bounds: 1999
                     variables with only upper bounds: 0
Total number of equality constraints.................: 4995
Total number of inequality constraints...............: 1000
        inequality constraints with only lower bounds: 1000
   inequality constraints with lower and upper bounds: 0
        inequality constraints with only upper bounds: 0

iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
   0 9.9999900e-03 1.56e+02 2.00e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
   1r 9.9999900e-03 1.56e+02 9.99e+02 0.2 0.00e+00 - 0.00e+00 3.33e-07R 4
   2r 1.9263008e-02 6.12e+01 9.98e+02 0.2 1.65e+03 - 1.22e-03 9.70e-04f 1
   3 1.9262650e-02 6.12e+01 3.20e+03 -1.0 6.13e+01 - 9.73e-05 1.69e-04f 1
   4 1.9262614e-02 6.12e+01 3.06e+03 -1.0 3.36e+02 - 4.14e-05 1.79e-05h 1
   5 1.9262503e-02 6.12e+01 2.87e+03 -1.0 5.90e+02 - 3.38e-05 5.45e-05h 1
   6 1.9262502e-02 6.12e+01 2.87e+03 -1.0 6.18e+02 - 1.23e-04 2.37e-07h 6
   7 1.9262502e-02 6.12e+01 2.87e+03 -1.0 5.82e+02 - 1.32e-04 2.87e-07h 6
   8 1.9262465e-02 6.12e+01 2.87e+03 -1.0 5.45e+02 - 6.34e-05 1.85e-05h 1
   9 1.9262456e-02 6.12e+01 2.87e+03 -1.0 4.80e+03 - 2.70e-06 4.24e-06f 2
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  10 1.9262456e-02 6.12e+01 2.99e+03 -1.0 4.90e+03 - 6.86e-06 2.63e-07h 5
  11 1.9262452e-02 6.12e+01 3.29e+03 -1.0 4.88e+03 - 4.94e-06 1.60e-06f 3
  12 1.9262451e-02 6.12e+01 3.83e+03 -1.0 4.85e+03 - 6.00e-06 6.11e-07h 4
  13 1.9262444e-02 6.12e+01 3.48e+03 -1.0 4.81e+03 - 5.26e-07 3.86e-06f 2
  14 1.9262436e-02 6.12e+01 3.30e+03 -1.0 4.86e+03 - 2.14e-06 3.72e-06f 2
  15r 1.9262436e-02 6.12e+01 1.00e+03 -0.4 0.00e+00 - 0.00e+00 4.60e-07R 5
  16r 2.5464204e-02 3.56e+01 9.99e+02 -0.4 5.23e+02 - 1.19e-03 5.15e-04f 1
  17 2.5464199e-02 3.56e+01 1.84e+01 -1.0 1.70e+02 - 7.36e-05 1.10e-05h 1
  18 2.5464182e-02 3.56e+01 5.50e+01 -1.0 5.87e+02 - 7.29e-06 3.93e-05f 1
  19r 2.5464182e-02 3.56e+01 9.99e+02 -0.6 0.00e+00 - 0.00e+00 4.49e-07R 4
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  20r 2.7129142e-02 3.30e+01 9.98e+02 -0.6 2.08e+02 - 1.32e-03 8.68e-05f 1
  21r 5.1678170e-02 1.20e+00 9.95e+02 -0.6 9.59e+01 - 3.38e-03 2.31e-03f 1
  22r 5.1678170e-02 1.20e+00 9.99e+02 -1.0 0.00e+00 - 0.00e+00 3.15e-07R 3
  23r 5.6729089e-02 1.18e+00 9.98e+02 -1.0 3.56e+01 - 1.77e-03 6.40e-04f 1
  24r 6.6002832e-02 1.14e+00 9.97e+02 -1.0 1.42e+01 - 1.58e-03 1.20e-03f 1
  25r 9.8505667e-02 9.98e-01 9.92e+02 -1.0 7.28e+00 - 5.20e-03 4.47e-03f 1
  26r 1.0225287e-01 9.87e-01 9.92e+02 -1.0 4.78e+00 - 5.96e-03 7.89e-04f 1
  27r 1.1636717e-01 9.44e-01 9.88e+02 -1.0 4.45e+00 - 3.90e-03 3.22e-03f 1
  28r 1.3177033e-01 8.84e-01 9.84e+02 -1.0 3.30e+00 - 4.43e-03 4.73e-03f 1
  29r 1.4160321e-01 8.19e-01 9.79e+02 -1.0 2.44e+00 - 5.28e-03 5.24e-03f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  30 1.4145724e-01 8.19e-01 2.55e+04 -1.0 5.48e+02 - 6.79e-05 2.14e-04f 1
  31 1.4096248e-01 8.19e-01 2.34e+04 -1.0 4.57e+02 - 1.35e-04 8.43e-04f 1
  32 1.4095301e-01 8.19e-01 2.34e+04 -1.0 3.28e+02 - 1.40e-04 1.17e-05h 1
  33 1.4078924e-01 8.19e-01 3.61e+05 -1.0 1.79e+03 - 3.25e-06 1.77e-04f 1
  34 1.4056815e-01 8.19e-01 5.35e+05 -1.0 9.60e+02 - 7.83e-05 2.49e-04f 1
  35 1.4037264e-01 8.19e-01 5.58e+05 -1.0 1.30e+03 - 7.61e-05 2.09e-04h 1
  36 1.4023681e-01 8.19e-01 7.31e+05 -1.0 2.47e+03 - 4.95e-05 1.32e-04h 1
  37 1.4016510e-01 8.19e-01 7.48e+05 -1.0 3.86e+03 - 3.59e-05 5.03e-05h 1
  38 1.4009700e-01 8.19e-01 1.04e+06 -1.0 6.74e+03 - 1.70e-05 3.96e-05h 1
  39 1.4005369e-01 8.19e-01 1.20e+06 -1.0 1.58e+04 - 7.56e-06 1.49e-05h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  40r 1.4005369e-01 8.19e-01 1.00e+03 -1.0 0.00e+00 - 0.00e+00 2.96e-07R 6
  41r 1.4136641e-01 7.99e-01 4.09e+03 -1.0 1.76e+00 - 9.82e-03 1.98e-03f 1
  42r 1.4730479e-01 6.38e-01 6.95e+03 -1.0 3.10e+00 - 3.85e-03 1.35e-02f 1
  43r 1.4730479e-01 6.38e-01 9.98e+02 -1.0 0.00e+00 - 0.00e+00 1.15e-07R 2
  44r 1.4779590e-01 5.25e-01 9.92e+02 -1.0 1.79e+00 - 1.24e-02 6.28e-03f 1
  45r 1.4843078e-01 3.49e-01 2.60e+03 -1.0 2.85e+00 - 6.70e-03 2.53e-02f 1
  46r 1.4782353e-01 2.71e-01 1.45e+03 -1.0 2.66e+00 - 8.47e-03 1.73e-02f 1
  47r 1.4758686e-01 2.52e-01 1.50e+03 -1.0 2.80e+00 - 8.44e-03 6.06e-03f 1
  48r 1.4745003e-01 2.44e-01 1.51e+03 -1.0 3.63e+00 - 6.47e-03 3.05e-03f 1
  49r 1.4717730e-01 2.33e-01 1.56e+03 -1.0 4.63e+00 - 5.01e-03 4.92e-03f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  50r 1.4678673e-01 2.20e-01 3.74e+03 -1.0 4.94e+00 - 5.58e-03 6.43e-03f 1
  51r 1.4575626e-01 1.88e-01 1.47e+04 -1.0 4.72e+00 - 6.02e-03 1.71e-02f 1
  52r 1.4566201e-01 1.80e-01 1.47e+04 -1.0 2.25e+00 - 6.27e-03 2.07e-03f 1
  53r 1.4548158e-01 1.70e-01 3.55e+04 -1.0 1.39e+00 2.0 5.53e-03 6.91e-03f 1
  54r 1.4539014e-01 1.27e-01 2.97e+04 -1.0 2.34e-02 4.2 1.06e-01 3.15e-02f 1
  55r 1.4533095e-01 1.18e-01 2.64e+04 -1.0 1.08e-01 3.8 2.99e-02 1.27e-02f 1
  56r 1.4512869e-01 7.71e-02 2.27e+04 -1.0 1.78e-02 4.2 1.28e-01 7.20e-02f 1
  57 1.4490266e-01 7.71e-02 7.08e+03 -1.0 1.54e+01 - 5.20e-03 5.83e-04f 1
  58 1.4452813e-01 7.71e-02 2.91e+05 -1.0 6.73e+02 - 1.48e-05 4.33e-04h 1
  59 1.4422222e-01 7.71e-02 4.49e+05 -1.0 6.49e+02 - 2.53e-04 2.27e-04h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  60 1.4370807e-01 7.71e-02 5.83e+05 -1.0 1.27e+03 - 1.31e-04 2.21e-04h 1
  61 1.4297321e-01 7.71e-02 5.92e+05 -1.0 7.02e+02 - 6.73e-05 1.25e-04h 1
  62 1.4072428e-01 7.71e-02 1.36e+06 -1.0 1.06e+03 - 1.31e-04 2.95e-04h 1
  63 1.2873821e-01 7.71e-02 4.49e+06 -1.0 1.04e+02 - 4.09e-04 1.68e-03f 1
  64 1.2871221e-01 7.71e-02 4.49e+06 -1.0 1.21e+02 - 4.74e-03 3.50e-05h 1
  65 1.2490836e-01 7.70e-02 7.36e+06 -1.0 4.20e+01 - 3.42e-03 4.95e-03f 1
  66 8.4787480e-02 7.64e-02 1.64e+07 -1.0 5.03e+00 - 4.98e-03 8.35e-02f 1
  67 7.8553840e-02 7.59e-02 1.47e+07 -1.0 6.66e+00 - 6.66e-02 6.69e-02f 1
  68 7.5543485e-02 7.56e-02 1.40e+07 -1.0 6.37e+00 - 1.49e-01 3.70e-02f 1
  69 7.5515373e-02 7.56e-02 3.49e+08 -1.0 6.19e+00 - 1.45e-01 3.64e-04h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  70 7.5512656e-02 7.56e-02 3.79e+11 -1.0 1.13e+01 - 3.81e-02 3.53e-05h 1
  71 7.5504268e-02 7.56e-02 6.40e+13 -1.0 1.57e+01 - 1.86e-02 1.09e-04h 1
  72r 7.5504268e-02 7.56e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 3.41e-07R 3
  73r 7.5563622e-02 7.53e-02 9.89e+03 -1.0 1.63e+01 - 1.05e-02 1.64e-03f 1
  74r 7.5792890e-02 7.31e-02 8.75e+03 -1.0 1.43e+01 - 5.81e-03 6.45e-03f 1
  75 7.3203256e-02 7.29e-02 4.82e+05 -1.0 6.13e+00 - 1.72e-01 3.35e-02f 1
  76 7.3162034e-02 7.29e-02 2.62e+08 -1.0 5.81e+00 - 1.83e-01 5.56e-04h 1
  77 7.2137141e-02 7.27e-02 5.87e+09 -1.0 5.61e+00 - 2.15e-01 1.39e-02h 1
  78 7.2100734e-02 7.27e-02 1.74e+12 -1.0 5.52e+00 - 1.40e-01 5.00e-04h 1
  79 7.2099621e-02 7.27e-02 2.64e+16 -1.0 5.52e+00 - 2.34e-01 1.53e-05h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  80r 7.2099621e-02 7.27e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 3.98e-07R 3
  81r 7.2182761e-02 7.15e-02 5.54e+03 -1.0 1.77e+01 - 7.29e-03 3.50e-03f 1
  82 7.1738248e-02 7.15e-02 1.79e+07 -1.0 5.74e+00 - 2.21e-01 6.10e-03f 1
  83 6.5183013e-02 7.07e-02 3.80e+08 -1.0 5.68e+00 - 3.96e-03 9.06e-02f 1
  84 6.5116414e-02 7.07e-02 3.91e+08 -1.0 5.20e+00 - 9.29e-02 1.02e-03h 1
  85 6.5115747e-02 7.07e-02 3.79e+08 -1.0 5.18e+00 - 1.41e-02 1.02e-05h 1
  86r 6.5115747e-02 7.07e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 4.93e-07R 4
  87r 6.5221569e-02 6.95e-02 6.98e+03 -1.0 2.05e+01 - 8.26e-03 2.34e-03f 1
  88 6.5182297e-02 6.95e-02 1.16e+07 -1.0 4.99e+00 - 3.10e-01 6.03e-04h 1
  89r 6.5182297e-02 6.95e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 3.78e-07R 5
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
  90r 6.5319853e-02 6.80e-02 5.63e+03 -1.0 1.96e+01 - 8.66e-03 3.07e-03f 1
  91 6.5266535e-02 6.80e-02 1.37e+07 -1.0 4.90e+00 - 3.20e-01 8.18e-04h 1
  92r 6.5266535e-02 6.80e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 2.56e-07R 6
  93r 6.5440982e-02 6.57e-02 4.73e+03 -1.0 1.85e+01 - 9.11e-03 4.01e-03f 1
  94 6.5368738e-02 6.57e-02 9.66e+06 -1.0 4.81e+00 - 2.94e-01 1.11e-03h 1
  95 6.5368015e-02 6.57e-02 2.36e+09 -1.0 4.80e+00 - 3.61e-01 1.11e-05h 1
  96r 6.5368015e-02 6.57e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 3.08e-07R 5
  97r 6.5504081e-02 6.31e-02 4.46e+03 -1.0 1.73e+01 - 1.05e-02 4.58e-03f 1
  98 6.5418433e-02 6.31e-02 6.84e+06 -1.0 4.71e+00 - 2.72e-01 1.31e-03h 1
  99 6.5417575e-02 6.31e-02 1.64e+09 -1.0 4.76e+00 - 3.63e-01 1.32e-05h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 100r 6.5417575e-02 6.31e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 3.48e-07R 5
 101r 6.5619873e-02 5.94e-02 4.52e+03 -1.0 1.58e+01 - 1.35e-02 6.84e-03f 1
 102r 6.6453038e-02 4.74e-02 1.11e+04 -1.0 1.17e+01 - 4.83e-02 2.89e-02f 1
 103r 6.7406490e-02 7.23e-02 9.49e+03 -1.0 4.55e+00 - 2.76e-02 3.52e-02f 1
 104r 6.7340988e-02 7.22e-02 2.76e+04 -1.0 3.44e-02 4.0 8.50e-02 3.51e-02f 1
 105r 6.7352639e-02 7.17e-02 2.73e+04 -1.0 4.13e+00 - 8.44e-04 4.11e-04f 1
 106r 6.7213982e-02 7.15e-02 1.56e+04 -1.0 6.13e-02 3.5 2.79e-02 5.72e-02f 1
 107r 6.7187230e-02 7.15e-02 2.61e+04 -1.0 5.92e-02 3.9 4.76e-02 1.52e-02f 1
 108r 6.7106847e-02 7.14e-02 3.45e+04 -1.0 4.31e-02 3.5 6.87e-02 3.47e-02f 1
 109r 6.7066182e-02 7.13e-02 3.33e+04 -1.0 1.50e-01 3.9 2.16e-02 2.35e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 110r 6.7006506e-02 7.13e-02 3.24e+04 -1.0 4.01e-02 3.4 2.69e-02 2.68e-02f 1
 111r 6.6859346e-02 7.12e-02 6.05e+04 -1.0 1.29e-02 3.8 2.01e-01 8.60e-02f 1
 112r 6.6575748e-02 7.09e-02 4.81e+04 -1.0 8.58e-03 4.3 2.85e-01 2.68e-01f 1
 113r 6.6559828e-02 7.09e-02 4.82e+04 -1.0 1.72e-01 3.8 2.11e-02 1.16e-02f 1
 114r 6.6364881e-02 7.06e-02 7.22e+04 -1.0 8.35e-03 4.2 5.17e-01 2.14e-01f 1
 115r 6.6121763e-02 7.02e-02 6.05e+04 -1.0 1.73e-03 4.6 1.00e+00 5.22e-01f 1
 116r 6.5586391e-02 6.86e-02 1.03e+04 -1.0 2.55e-03 4.2 1.00e+00 8.02e-01f 1
 117r 6.4949064e-02 6.44e-02 9.59e+03 -1.0 4.71e-03 3.7 1.00e+00 1.00e+00f 1
 118r 6.4885306e-02 5.76e-02 3.22e+04 -1.0 1.47e-02 3.2 1.00e+00 7.92e-01f 1
 119r 6.4897911e-02 5.40e-02 7.87e+03 -1.0 3.55e-03 3.6 1.00e+00 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 120r 6.5282534e-02 4.66e-02 1.16e+04 -1.0 7.48e-03 3.2 1.00e+00 1.00e+00f 1
 121r 6.7015934e-02 3.28e-02 7.20e+03 -1.0 1.37e-02 2.7 1.00e+00 1.00e+00f 1
 122r 7.2635183e-02 2.45e-02 1.05e+04 -1.0 2.59e-02 2.2 1.00e+00 1.00e+00f 1
 123r 7.3336436e-02 3.01e-02 3.51e+04 -1.0 9.95e-01 1.7 5.47e-02 6.05e-02F 1
 124r 7.4118433e-02 3.05e-02 1.88e+04 -1.0 5.77e-03 3.1 1.00e+00 1.00e+00f 1
 125r 7.5881054e-02 2.96e-02 1.00e+04 -1.0 1.32e-02 2.6 9.48e-01 7.60e-01f 1
 126r 7.5952551e-02 2.96e-02 2.88e+03 -1.0 1.86e-03 3.9 1.00e+00 6.56e-01f 1
 127r 7.6279414e-02 2.94e-02 8.69e+02 -1.0 1.85e-03 3.4 1.00e+00 1.00e+00f 1
 128r 7.7252002e-02 2.88e-02 5.05e+02 -1.0 5.53e-03 3.0 1.00e+00 1.00e+00f 1
 129r 8.0052578e-02 2.79e-02 2.40e+03 -1.0 1.67e-02 2.5 1.00e+00 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 130r 8.2021764e-02 2.83e-02 8.20e+04 -1.0 1.13e-01 2.0 3.19e-01 2.77e-01F 1
 131r 8.4876875e-02 2.83e-02 1.58e+04 -1.0 1.90e-02 2.4 1.00e+00 1.00e+00f 1
 132 8.0249864e-02 2.67e-02 1.25e+04 -1.0 2.50e+00 - 7.13e-02 5.54e-02h 1
 133 7.4636193e-02 2.45e-02 3.46e+04 -1.0 3.00e+00 - 8.77e-02 7.12e-02h 1
 134 7.3809769e-02 2.41e-02 7.25e+05 -1.0 2.49e+00 - 1.74e-01 1.13e-02h 1
 135 7.3798438e-02 2.41e-02 5.19e+07 -1.0 7.94e+00 - 9.89e-03 1.56e-04h 1
 136 7.3620037e-02 2.41e-02 1.10e+07 -1.0 1.49e+02 - 6.02e-04 2.45e-03h 1
 137 7.3605855e-02 2.40e-02 2.11e+09 -1.0 9.24e+01 - 4.43e-03 1.95e-04h 1
 138 7.3599343e-02 2.40e-02 2.14e+10 -1.0 4.53e+02 - 8.43e-04 8.97e-05h 1
 139r 7.3599343e-02 2.40e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 4.49e-07R 4
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 140r 7.4408520e-02 2.43e-02 1.01e+04 -1.0 5.67e-01 - 6.63e-02 1.97e-02f 1
 141r 7.7821300e-02 3.19e-02 1.31e+04 -1.0 4.34e-01 - 1.27e-01 8.13e-02f 1
 142 7.7333980e-02 3.17e-02 5.09e+05 -1.0 2.07e+00 - 1.28e-01 6.37e-03f 1
 143 7.7291431e-02 3.17e-02 1.49e+08 -1.0 3.55e+00 - 1.10e-01 5.59e-04h 1
 144 7.6515671e-02 3.14e-02 2.88e+09 -1.0 3.36e+00 - 1.82e-01 1.02e-02h 1
 145 7.6487635e-02 3.14e-02 1.20e+11 -1.0 2.92e+01 - 1.48e-02 3.73e-04h 1
 146r 7.6487635e-02 3.14e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 4.25e-07R 5
 147r 7.8138416e-02 3.54e-02 1.80e+04 -1.0 4.35e-01 - 1.71e-01 4.45e-02f 1
 148r 8.3135749e-02 4.69e-02 7.66e+04 -1.0 4.92e-01 - 7.66e-01 1.27e-01f 1
 149 7.9891006e-02 4.59e-02 2.42e+05 -1.0 3.41e+00 - 8.57e-02 3.96e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 150 7.8120496e-02 4.53e-02 1.72e+07 -1.0 2.43e+00 - 5.26e-01 2.25e-02h 1
 151 7.8075810e-02 4.53e-02 7.19e+09 -1.0 2.35e+00 - 2.22e-01 5.81e-04h 1
 152 7.7942727e-02 4.52e-02 8.56e+11 -1.0 2.28e+00 - 2.06e-01 1.73e-03h 1
 153 7.7940793e-02 4.52e-02 2.89e+16 -1.0 2.72e+00 - 8.52e-01 2.52e-05h 1
 154r 7.7940793e-02 4.52e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 1.40e-07R 2
 155r 7.8114585e-02 4.55e-02 6.99e+04 -1.0 1.59e+00 - 2.28e-01 9.50e-03f 3
 156r 8.3677416e-02 6.22e-02 8.70e+04 -1.0 1.58e+00 - 9.92e-01 2.53e-01f 1
 157 8.3635098e-02 6.22e-02 2.59e+06 -1.0 2.04e+00 - 5.89e-01 5.12e-04f 5
 158 8.2999202e-02 6.20e-02 2.51e+08 -1.0 2.09e+00 - 7.47e-01 7.70e-03h 1
 159 8.1933530e-02 6.16e-02 6.76e+09 -1.0 1.18e+00 - 3.47e-01 1.30e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 160 8.1807679e-02 6.16e-02 3.37e+12 -1.0 1.66e+00 - 7.56e-01 1.56e-03h 1
 161 8.1805967e-02 6.16e-02 2.54e+16 -1.0 2.93e+00 - 1.61e-01 2.12e-05h 1
 162 8.1805967e-02 6.16e-02 2.51e+14 -1.0 6.77e-09 16.0 9.90e-01 1.00e+00h 1
 163r 8.1805967e-02 6.16e-02 1.00e+03 -1.0 0.00e+00 - 0.00e+00 1.17e-07R 2
 164r 8.6400165e-02 6.59e-02 1.10e+05 -1.0 1.39e+00 - 6.83e-01 1.21e-01f 1
 165r 1.2303118e-01 8.53e-02 3.10e+04 -1.0 1.16e+00 - 8.31e-01 7.64e-01f 1
 166r 1.2359049e-01 9.10e-02 3.79e+04 -1.0 1.36e-02 2.0 8.58e-01 3.33e-01f 1
 167r 1.2396345e-01 8.75e-02 1.06e+04 -1.0 1.38e-02 2.4 1.00e+00 5.88e-01f 1
 168r 1.2575264e-01 7.05e-02 4.85e+02 -1.0 2.22e-02 1.9 1.00e+00 1.00e+00f 1
 169r 1.2983673e-01 3.79e-02 3.03e+02 -1.0 5.61e-02 1.5 1.00e+00 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 170r 1.2989395e-01 3.80e-02 3.13e+03 -1.0 3.45e+00 1.0 2.91e-02 8.66e-03f 3
 171r 1.2996510e-01 3.76e-02 6.80e+02 -1.0 1.11e-03 3.2 1.00e+00 1.00e+00f 1
 172r 1.3017631e-01 3.71e-02 7.92e+01 -1.0 2.29e-03 2.7 1.00e+00 1.00e+00f 1
 173r 1.3078032e-01 3.29e-02 1.76e+01 -1.0 6.28e-03 2.3 1.00e+00 1.00e+00f 1
 174r 1.3234891e-01 2.34e-02 5.98e+02 -1.0 3.11e-02 1.8 1.00e+00 1.00e+00f 1
 175r 1.3259492e-01 2.27e-02 3.69e+04 -1.0 4.00e-01 1.3 3.10e-01 7.58e-02f 2
 176r 1.3406520e-01 1.40e-02 3.84e+01 -1.0 3.73e-02 1.7 1.00e+00 1.00e+00f 1
 177r 1.3697540e-01 1.21e-02 1.90e+02 -1.0 8.43e-02 1.3 1.00e+00 1.00e+00f 1
 178r 1.3790207e-01 1.20e-02 6.40e+01 -1.0 1.42e-02 1.7 1.00e+00 1.00e+00f 1
 179r 1.3969952e-01 1.32e-02 8.38e+02 -1.0 4.38e-02 1.2 1.00e+00 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 180r 1.4026468e-01 1.39e-02 2.09e+02 -1.0 1.94e-02 1.6 1.00e+00 1.00e+00f 1
 181r 1.4046219e-01 1.43e-02 4.53e+01 -1.0 7.58e-03 2.1 1.00e+00 1.00e+00f 1
 182r 1.4095097e-01 1.56e-02 1.16e+03 -1.0 4.18e-02 1.6 1.00e+00 1.00e+00f 1
 183r 1.4112123e-01 1.63e-02 6.22e+01 -1.0 2.16e-02 2.0 1.00e+00 1.00e+00f 1
 184r 1.4153884e-01 1.81e-02 3.22e+02 -1.0 6.21e-02 1.5 1.00e+00 1.00e+00f 1
 185r 1.4168358e-01 1.88e-02 6.74e+01 -1.0 1.92e-02 2.0 1.00e+00 1.00e+00f 1
 186r 1.4183622e-01 2.03e-02 3.63e+03 -1.0 1.00e-01 1.5 6.33e-01 4.30e-01f 2
 187r 1.4197415e-01 2.12e-02 3.52e+01 -1.0 2.48e-02 1.9 1.00e+00 1.00e+00f 1
 188r 1.4229977e-01 2.50e-02 2.57e+02 -1.0 6.82e-02 1.4 1.00e+00 1.00e+00f 1
 189r 1.4263582e-01 5.60e-02 4.48e+03 -1.0 1.04e-01 1.0 1.00e+00 7.62e-01F 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 190r 1.4265834e-01 6.84e-02 1.68e+03 -1.0 1.53e-02 2.3 1.00e+00 8.85e-01h 1
 191r 1.4272531e-01 7.28e-02 8.14e+01 -1.0 2.52e-02 1.8 1.00e+00 1.00e+00f 1
 192r 1.4283214e-01 1.08e-01 1.35e+03 -1.0 6.73e-02 1.3 1.00e+00 1.00e+00f 1
 193r 1.4281762e-01 1.07e-01 9.84e+03 -1.0 8.82e-01 0.9 1.29e-01 4.01e-02f 3
 194r 1.4280315e-01 1.19e-01 1.36e+03 -1.0 4.68e-02 1.3 1.00e+00 1.00e+00f 1
 195r 1.4254558e-01 1.11e-01 1.11e+03 -1.0 8.02e-02 0.8 1.00e+00 1.00e+00f 1
 196r 1.4244677e-01 1.08e-01 4.27e+01 -1.0 1.80e-02 1.2 1.00e+00 1.00e+00f 1
 197r 1.4226538e-01 1.04e-01 1.32e+02 -1.0 4.53e-02 0.8 1.00e+00 1.00e+00f 1
 198r 1.4221142e-01 1.01e-01 5.69e+01 -1.0 1.43e-02 1.2 1.00e+00 1.00e+00f 1
 199r 1.4220172e-01 1.01e-01 4.59e+03 -1.0 9.52e-02 0.7 1.00e+00 2.50e-01f 3
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 200r 1.4220122e-01 1.00e-01 1.71e+04 -1.0 8.56e-02 1.1 1.00e+00 1.25e-01f 4
 201r 1.4218741e-01 9.95e-02 2.91e+00 -1.0 7.11e-03 1.6 1.00e+00 1.00e+00f 1
 202r 1.2582161e-01 1.03e-01 1.30e+04 -1.7 1.46e-01 1.1 3.74e-01 3.62e-01f 1
 203r 1.1051968e-01 1.15e-01 3.68e+04 -1.7 3.54e-02 1.5 8.71e-01 6.59e-01f 1
 204r 1.0129625e-01 1.44e-01 2.96e+04 -1.7 1.57e-02 1.9 1.00e+00 8.47e-01f 1
 205r 9.7073006e-02 1.42e-01 2.51e+04 -1.7 1.73e-01 1.5 2.22e-01 1.83e-01f 1
 206r 8.7124928e-02 1.35e-01 8.58e+03 -1.7 1.16e-02 1.9 1.00e+00 1.00e+00f 1
 207r 8.3201403e-02 1.23e-01 7.37e+03 -1.7 1.20e-01 1.4 2.49e-01 2.11e-01f 1
 208r 7.5093725e-02 8.20e-02 2.73e+03 -1.7 1.63e-02 1.8 1.00e+00 1.00e+00f 1
 209r 6.9950640e-02 3.25e-02 2.90e+03 -1.7 8.71e-02 1.4 4.35e-01 3.41e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 210r 6.4656153e-02 7.45e-03 2.10e+03 -1.7 1.43e-02 1.8 1.00e+00 7.91e-01f 1
 246 2.8072332e-03 1.66e-05 2.49e+06 -1.0 2.22e-01 - 1.00e+00 4.81e-02h 5
 247 2.8349267e-03 1.57e-05 2.70e+06 -1.0 2.04e-01 - 1.00e+00 4.84e-02h 5
 248 2.8629932e-03 1.50e-05 2.90e+06 -1.0 1.97e-01 - 1.00e+00 4.84e-02h 5
 249 2.8917742e-03 1.43e-05 3.07e+06 -1.0 1.89e-01 - 1.00e+00 4.84e-02h 5
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 250 3.3664069e-03 6.69e-05 1.57e+06 -1.0 1.81e-01 - 1.00e+00 7.75e-01w 1
 251 5.5300533e-03 1.11e-03 1.02e+07 -1.0 1.30e+00 - 2.62e-01 9.87e-01w 1
 252 1.0629220e-02 3.18e-03 3.01e+06 -1.0 1.57e+00 - 3.65e-01 1.00e+00w 1
 253 2.9511033e-03 1.29e-05 3.06e+06 -1.0 3.26e-01 - 1.00e+00 9.68e-02h 3
 254 2.9848641e-03 1.23e-05 3.84e+06 -1.0 1.66e-01 - 1.00e+00 4.81e-02h 5
 255 3.0190653e-03 1.17e-05 4.72e+06 -1.0 1.54e-01 - 1.00e+00 4.87e-02h 5
 256 3.0542668e-03 1.11e-05 5.78e+06 -1.0 1.47e-01 - 1.00e+00 4.89e-02h 5
 257 3.0906899e-03 1.05e-05 7.03e+06 -1.0 1.39e-01 - 1.00e+00 4.91e-02h 5
 258 3.1095384e-03 1.03e-05 8.72e+06 -1.0 1.32e-01 - 1.00e+00 2.47e-02h 6
 259 3.1468402e-03 9.78e-06 1.04e+07 -1.0 1.29e-01 - 1.00e+00 4.97e-02h 5
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 260 3.1665035e-03 9.53e-06 1.28e+07 -1.0 1.38e-01 - 1.00e+00 2.49e-02h 6
 261 3.2055680e-03 9.07e-06 1.51e+07 -1.0 1.24e-01 - 1.00e+00 5.02e-02h 5
 262 3.2262213e-03 8.85e-06 1.83e+07 -1.0 1.60e-01 - 1.00e+00 2.52e-02h 6
 263 3.8835449e-03 4.04e-05 7.93e+06 -1.0 1.48e-01 - 1.00e+00 8.14e-01w 1
 264 5.8638686e-03 1.20e-03 1.62e+08 -1.0 1.17e+00 - 1.19e-01 1.00e+00w 1
 265 9.7329055e-03 2.80e-03 2.36e+06 -1.0 1.35e+00 - 8.82e-01 1.00e+00w 1
 266 3.2467627e-03 8.62e-06 2.19e+07 -1.0 1.50e+00 - 1.00e+00 2.54e-02h 5
 267 3.2675339e-03 8.41e-06 2.60e+07 -1.0 1.51e-01 - 1.00e+00 2.55e-02h 6
 268 3.2886208e-03 8.20e-06 3.08e+07 -1.0 1.59e-01 - 1.00e+00 2.57e-02h 6
 269 3.3100455e-03 7.99e-06 3.63e+07 -1.0 1.67e-01 - 1.00e+00 2.58e-02h 6
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 270 3.3318361e-03 7.78e-06 4.25e+07 -1.0 1.77e-01 - 1.00e+00 2.59e-02h 6
 312 4.0689751e-03 4.78e-06 2.09e+08 -1.0 6.42e-01 - 1.00e+00 1.56e-02h 7
 313 4.0906299e-03 4.81e-06 1.95e+08 -1.0 6.55e-01 - 1.00e+00 1.56e-02h 7
 314 4.1126371e-03 4.83e-06 1.80e+08 -1.0 6.68e-01 - 1.00e+00 1.56e-02h 7
 315 5.5446739e-03 4.27e-04 3.22e+07 -1.0 6.81e-01 - 1.00e+00 1.00e+00w 1
 316 1.0125712e-02 4.28e-03 1.16e+09 -1.0 1.95e+00 - 1.95e-01 1.00e+00w 1
 317 1.6101826e-02 1.38e-04 1.31e+06 -1.0 2.15e-01 - 1.00e+00 1.00e+00w 1
 318 4.1350127e-03 4.86e-06 1.64e+08 -1.0 8.33e-01 - 1.00e+00 1.56e-02h 6
 319 4.1577748e-03 4.89e-06 1.48e+08 -1.0 6.94e-01 - 1.00e+00 1.56e-02h 7
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 320 4.1693598e-03 4.88e-06 1.33e+08 -1.0 7.08e-01 - 1.00e+00 7.81e-03h 8
 321 4.1810345e-03 4.87e-06 1.17e+08 -1.0 7.12e-01 - 1.00e+00 7.81e-03h 8
 322 4.1928460e-03 4.86e-06 1.03e+08 -1.0 7.20e-01 - 1.00e+00 7.81e-03h 8
 323 4.2048136e-03 4.85e-06 8.88e+07 -1.0 7.28e-01 - 1.00e+00 7.81e-03h 8
 324 4.2169515e-03 4.85e-06 7.57e+07 -1.0 7.37e-01 - 1.00e+00 7.81e-03h 8
 325 4.2292851e-03 4.84e-06 6.35e+07 -1.0 7.47e-01 - 1.00e+00 7.81e-03h 8
 326 4.2418574e-03 4.83e-06 5.25e+07 -1.0 7.59e-01 - 1.00e+00 7.81e-03h 8
 327 4.2547649e-03 4.82e-06 4.32e+07 -1.0 7.73e-01 - 1.00e+00 7.81e-03h 8
 328 5.9950385e-03 5.45e-04 5.75e+06 -1.0 8.00e-01 - 7.71e-01 1.00e+00w 1
 329 6.6127800e-03 5.45e-04 1.76e+07 -1.0 8.41e+01 - 3.70e-04 4.93e-03w 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 330 7.5349653e-03 4.38e-07 1.85e+17 -1.0 5.32e-03 15.5 1.53e-01 1.00e+00h 1
MUMPS returned INFO(1) = -9 and requires more memory, reallocating. Attempt 1
  Increasing icntl[13] from 1000 to 2000.
MUMPS returned INFO(1) = -9 and requires more memory, reallocating. Attempt 2
  Increasing icntl[13] from 2000 to 4000.
 331 7.5575806e-03 2.73e-09 8.70e+15 -1.0 7.81e-04 15.0 1.00e+00 1.00e+00f 1
 332 7.5575628e-03 7.99e-15 3.78e+11 -1.0 1.28e-06 14.6 1.00e+00 1.00e+00h 1
 333 7.5575628e-03 4.44e-16 2.79e+02 -1.7 2.26e-12 14.1 1.00e+00 1.00e+00h 1
 334 7.5575628e-03 4.44e-16 4.85e+00 -5.7 1.18e-13 13.6 1.00e+00 1.00e+00h 1
 335 7.5575628e-03 4.44e-16 2.50e-02 -5.7 1.83e-15 13.1 1.00e+00 1.00e+00 0
 336 7.5575628e-03 4.44e-16 4.61e-03 -5.7 1.01e-15 12.7 1.00e+00 1.00e+00 0
 337 7.5575628e-03 4.44e-16 5.70e-04 -5.7 3.74e-16 12.2 1.00e+00 1.00e+00 0
 338 7.5575628e-03 4.44e-16 5.44e-04 -5.7 1.07e-15 11.7 1.00e+00 1.00e+00 0
 339 7.5575628e-03 4.44e-16 5.17e-04 -5.7 3.05e-15 11.2 1.00e+00 1.00e+00 0
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 340 7.5575628e-03 4.44e-16 5.25e-04 -5.7 9.31e-15 10.8 1.00e+00 1.00e+00h 1
 341 7.5575628e-03 4.44e-16 5.29e-04 -5.7 2.81e-14 10.3 1.00e+00 1.00e+00h 1
 342 7.5575628e-03 4.44e-16 5.26e-04 -5.7 8.38e-14 9.8 1.00e+00 1.00e+00h 1
 343 7.5575628e-03 4.44e-16 5.24e-04 -5.7 2.51e-13 9.3 1.00e+00 1.00e+00h 1
 344 7.5575628e-03 4.44e-16 5.25e-04 -5.7 7.53e-13 8.8 1.00e+00 1.00e+00h 1
 345 7.5575628e-03 4.44e-16 5.25e-04 -5.7 2.26e-12 8.4 1.00e+00 1.00e+00h 1
 346 7.5575628e-03 4.44e-16 5.25e-04 -5.7 6.78e-12 7.9 1.00e+00 1.00e+00h 1
 347 7.5575628e-03 4.44e-16 5.25e-04 -5.7 2.03e-11 7.4 1.00e+00 1.00e+00h 1
 348 7.5575628e-03 4.44e-16 5.25e-04 -5.7 6.10e-11 6.9 1.00e+00 1.00e+00h 1
 349 7.5575628e-03 4.44e-16 5.25e-04 -5.7 1.83e-10 6.5 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 350 7.5575628e-03 4.44e-16 5.25e-04 -5.7 5.49e-10 6.0 1.00e+00 1.00e+00h 1
 351 7.5575628e-03 4.44e-16 5.25e-04 -5.7 1.65e-09 5.5 1.00e+00 1.00e+00h 1
 352 7.5575628e-03 4.44e-16 5.25e-04 -5.7 4.94e-09 5.0 1.00e+00 1.00e+00h 1
 353 7.5575628e-03 4.44e-16 5.25e-04 -5.7 1.48e-08 4.5 1.00e+00 1.00e+00h 1
 354 7.5575629e-03 4.44e-16 5.25e-04 -5.7 4.45e-08 4.1 1.00e+00 1.00e+00h 1
 355 7.5575629e-03 4.44e-16 5.25e-04 -5.7 1.33e-07 3.6 1.00e+00 1.00e+00h 1
 356 7.5575630e-03 4.44e-16 5.25e-04 -5.7 4.00e-07 3.1 1.00e+00 1.00e+00h 1
 357 7.5575633e-03 5.69e-16 5.25e-04 -5.7 1.20e-06 2.6 1.00e+00 1.00e+00h 1
 358 7.5575641e-03 5.18e-15 5.24e-04 -5.7 3.60e-06 2.2 1.00e+00 1.00e+00h 1
 359 7.5575667e-03 4.64e-14 5.23e-04 -5.7 1.08e-05 1.7 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 360 7.5575746e-03 4.15e-13 5.21e-04 -5.7 3.22e-05 1.2 1.00e+00 1.00e+00h 1
 361 7.5575981e-03 3.67e-12 5.12e-04 -5.7 9.49e-05 0.7 1.00e+00 1.00e+00h 1
 362 7.5576693e-03 3.14e-11 4.89e-04 -5.7 2.72e-04 0.3 1.00e+00 1.00e+00h 1
 363 7.5578876e-03 2.47e-10 4.34e-04 -5.7 7.24e-04 -0.2 1.00e+00 1.00e+00h 1
 364 7.5585735e-03 1.68e-09 1.84e-03 -5.7 1.70e-03 -0.7 1.00e+00 1.00e+00h 1
 365 7.5607791e-03 9.50e-09 6.74e-03 -5.7 3.56e-03 -1.2 1.00e+00 1.00e+00h 1
 366 7.5678705e-03 4.57e-08 1.93e-02 -5.7 7.12e-03 -1.7 1.00e+00 1.00e+00h 1
 367 7.5902322e-03 2.24e-07 4.07e-02 -5.7 1.39e-02 -2.1 1.00e+00 1.00e+00h 1
 368 7.6594408e-03 2.05e-06 7.09e-02 -5.7 2.66e-02 -2.6 1.00e+00 1.00e+00h 1
 369 7.8736336e-03 1.94e-05 1.17e-01 -5.7 7.37e-02 -3.1 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 370 8.5895324e-03 2.15e-04 1.94e-01 -5.7 2.39e-01 -3.6 1.00e+00 1.00e+00h 1
 371 1.0568509e-02 1.63e-03 2.92e+00 -5.7 1.13e+00 -4.0 9.01e-01 5.25e-01h 1
 372 1.3005687e-02 7.79e-04 4.97e-01 -5.7 3.94e-01 -3.6 1.00e+00 1.00e+00f 1
 373 1.6306827e-02 1.60e-03 6.32e+00 -5.7 3.32e+00 -4.1 3.45e-01 1.38e-01h 1
 374 2.0759846e-02 1.31e-03 4.42e+00 -5.7 6.65e-01 -3.7 1.00e+00 5.26e-01h 1
 375 2.5548539e-02 2.62e-04 7.68e-01 -5.7 2.33e-01 -3.2 1.00e+00 9.70e-01f 1
 376 3.1550045e-02 1.21e-03 6.07e+00 -5.7 1.30e+00 -3.7 6.77e-01 2.22e-01f 1
 377 4.0770508e-02 9.00e-03 1.39e+01 -5.7 5.18e+02 -4.2 4.01e-04 5.02e-04f 1
 378 5.6349896e-02 1.98e-02 1.17e+02 -5.7 4.82e-01 -3.8 3.23e-01 1.00e+00f 1
 379 6.0645344e-02 1.95e-02 1.15e+02 -5.7 1.98e+01 - 7.16e-03 1.54e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 380 6.6253489e-02 1.88e-02 1.11e+02 -5.7 5.16e+00 -4.2 3.69e-02 3.77e-02h 1
 381 7.7560176e-02 1.77e-02 1.05e+02 -5.7 4.42e+00 -3.8 2.48e-02 5.62e-02f 1
 382 9.8290149e-02 9.22e-03 5.73e+01 -5.7 5.59e-01 -3.4 3.41e-01 4.97e-01f 1
 383 1.0750273e-01 8.91e-03 5.54e+01 -5.7 5.22e+00 -3.9 2.62e-02 3.38e-02h 1
 384 1.2607729e-01 6.69e-03 4.26e+01 -5.7 1.21e+00 -3.4 1.24e-01 2.51e-01f 1
 385 1.5119624e-01 5.88e-03 3.72e+01 -5.7 3.27e+00 -3.9 2.70e-02 1.53e-01f 1
 386 1.5186515e-01 5.35e-03 3.50e+01 -5.7 1.85e+00 - 9.41e-02 1.00e-01h 1
 387 1.5116854e-01 5.17e-03 3.34e+01 -5.7 3.65e+00 - 8.44e-02 3.31e-02h 1
 388 1.5026803e-01 4.88e-03 3.08e+01 -5.7 2.86e+00 - 1.65e-01 5.59e-02h 1
 389 1.4653227e-01 3.02e-03 1.66e+01 -5.7 7.02e-01 - 1.57e-01 4.11e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 390 1.4732849e-01 2.26e-03 1.11e+01 -5.7 5.33e-01 - 3.58e-01 3.16e-01h 1
 391 1.5068781e-01 7.33e-04 1.06e+01 -5.7 1.91e-01 - 8.26e-01 1.00e+00h 1
 392 1.5212574e-01 3.18e-04 1.73e+00 -5.7 2.71e-01 - 8.46e-01 7.65e-01h 1
 393 1.5206265e-01 1.44e-04 5.14e-01 -5.7 1.98e-01 - 1.00e+00 1.00e+00f 1
 394 1.5115643e-01 3.49e-05 9.01e-02 -5.7 8.57e-02 - 1.00e+00 1.00e+00h 1
 395 1.5088075e-01 1.95e-06 4.58e-03 -5.7 1.05e-02 - 1.00e+00 1.00e+00h 1
 396 1.5086729e-01 5.32e-09 1.26e-05 -5.7 6.87e-04 - 1.00e+00 1.00e+00h 1
 397 1.5102879e-01 5.96e-06 2.68e+01 -8.6 6.23e-02 - 8.51e-01 1.00e+00h 1
 398 1.5105075e-01 1.22e-05 8.31e+00 -8.6 1.26e-01 - 6.90e-01 1.00e+00h 1
 399 1.5105609e-01 8.66e-06 2.52e+00 -8.6 1.38e-01 - 6.97e-01 9.99e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
 400 1.5105708e-01 5.07e-06 9.56e-01 -8.6 2.65e-01 - 6.20e-01 4.93e-01h 1
 401 1.5105818e-01 2.65e-06 5.51e-01 -8.6 3.28e-01 - 4.24e-01 7.56e-01f 1
 402 1.5105850e-01 9.56e-07 2.77e-01 -8.6 6.52e-02 - 4.97e-01 7.78e-01f 1
 403 1.5105872e-01 5.92e-07 2.12e-03 -8.6 9.67e-02 - 1.00e+00 1.00e+00f 1
 404 1.5105875e-01 2.47e-07 1.58e-04 -8.6 3.97e-02 - 1.00e+00 1.00e+00h 1
 405 1.5105875e-01 1.38e-09 4.24e-07 -8.6 4.29e-03 - 1.00e+00 1.00e+00h 1
 406 1.5105875e-01 4.89e-13 7.06e-11 -8.6 8.47e-05 - 1.00e+00 1.00e+00h 1

Number of Iterations....: 406

                                   (scaled) (unscaled)
Objective...............: -1.5105874963825716e-01 1.5105874963825716e-01
Dual infeasibility......: 7.0607512892006952e-11 7.0607512892006952e-11
Constraint violation....: 4.8877568659122517e-13 4.8877568659122517e-13
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 2.5059039019713751e-09 2.5059039019713751e-09
Overall NLP error.......: 2.5059039019713751e-09 2.5059039019713751e-09

Number of objective function evaluations = 1045
Number of objective gradient evaluations = 306
Number of equality constraint evaluations = 1045
Number of inequality constraint evaluations = 1045
Number of equality constraint Jacobian evaluations = 424
Number of inequality constraint Jacobian evaluations = 424
Number of Lagrangian Hessian evaluations = 406
Total seconds in IPOPT = 27.202

EXIT: Optimal Solution Found.

```

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 8, 2024, 3:17am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/10 "2024-03-08T03:17:21Z")

</div>

> [@lpz18](#):
>
> my intution is that it’s taking a long time due to the fact that the added DEs have terms that have very large and very small magnitudes

Part of it is the numerics. Part of it is also how the `du` expressions are nested. Extracting the `du` into decision variables cuts the number of iterations required in half:

```Julia
function integration_JuMP!(model, u, du, jc, ::TrapezoidalIntegrationRule)
    @constraint(
        model,
        [t in 2:jc.n, k in 1:length(u)],
        u[k][t] == u[k][t-1] + 0.5 * jc.Δt * (du[k][t-1] + du[k][t]),
    )
    return
end

function slow_sim(u0, jc::JumpConfig; Kd = 1e-6, k_on = 4e6, C_max = 1e-6)
    n = jc.n
    model = Model(Ipopt.Optimizer)
    set_silent(model)
    u = @variables(model,begin
        0 <= φ_R[1:n] <= 0.45
        0 <= c_pc[1:n]
        0 <= C_bnd[1:n]
        0 <= C_in[1:n]
        0 <= M[1:n]
    end);
    for i in 1:length(u)
        fix(u[i][1], u0[i]; force = true)
    end
    @variable(model, 0 <= α_R[1:n] <= 0.45)
    @expressions(model, begin
        C_Rf, 6.4e-5 .* φ_R .- C_bnd
        φ_Rf, φ_R .- C_bnd ./ 6.4e-5
        φ_M, 0.45 .- φ_R
        γ, 10 .* c_pc ./ (c_pc .+ 0.03)
        λ, γ .* φ_Rf
    end)
    @constraint(model, φ_Rf .>= 0)
    k_off = k_on * Kd
    du = [@variable(model, [1:n]) for _ in 1:length(u0)]
    @constraints(model, begin
        du[1] .== (α_R .- φ_R) .* λ
        du[2] .== 5 .* (0.45 .- φ_R) .- (1 .+ c_pc) .* λ
        du[3] .== k_on .* C_in .* C_Rf - k_off .* C_bnd .- λ .* C_bnd
        du[4] .== 1.5 .* (C_max .- C_in) + k_off .* C_bnd .- k_on .* C_Rf .* C_in .- λ .* C_in
        du[5] .== M .* λ
    end)
    integration_JuMP!(model, u, du, jc, TrapezoidalIntegrationRule())
    @objective(model, Max, M[n])
    optimize!(model)
    @assert is_solved_and_feasible(model)
    Rs = value.(φ_R)
    a_Rs = value.(α_R)
    cpcs = value.(c_pc)
    C_bnds = value.(C_bnd)
    C_ins = value.(C_in)
    Ls = value.(λ)
    return Rs, a_Rs, cpcs, C_bnds, C_ins, Ls
end

```

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 3:22am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/11 "2024-03-08T03:22:47Z")

</div>

thanks 🙂 , that’s a huge improvement!

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 3:25am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/12 "2024-03-08T03:25:04Z")

</div>

what do you mean “decision variables”

what I got from seeing your changes is that lumping the expressions and the constraints into one macro call + not double defining `du[i]` with a second name reduces the overhead?

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 8, 2024, 3:27am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/13 "2024-03-08T03:27:21Z")

</div>

> [@odow](#):
>
> `du = [@variable(model, [1:n]) for _ in 1:length(u0)]`

I created `du` as a decision variable (a column in the model).

This results in more variables in the model, but simpler constraints, since your integration constraints are now linear, and the nonlinearity is restricted to the `@constraints` block with `du`.

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 8, 2024, 3:28am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/14 "2024-03-08T03:28:39Z")

</div>

You should carefully check whether the solutions make sense though. Ipopt has a tolerance of `1e-8`, so you may be getting weird solutions if you have very large and very small data coefficients.

---

<div class="post-metadata">

**Author:** ![gdalle](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/gdalle/32/27854_2.png) [@gdalle](https://discourse.julialang.org/u/gdalle)\
**Post date:** [March 8, 2024, 6:15am UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/15 "2024-03-08T06:15:45Z")

</div>

Perhaps a stupid question but why use JuMP to solve differential equations instead of DifferentialEquations.jl?

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 6:26pm UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/16 "2024-03-08T18:26:42Z")

</div>

I am using JuMP to find the optimal control of the system – similarly to the rocket control eample in the docs.

In other scripts I am also using DifferentialEquations.jl to experiment with different control laws, but JuMP is giving me a reference for what is optimal

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 6:43pm UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/17 "2024-03-08T18:43:49Z")

</div>

yesterday it ran much faster (~20s) with the changes you suggested, but today it’s back to taking much longer (~180s) and I haven’t changed anything.

here’s the Ipopt log:

```julia
This is Ipopt version 3.14.14, running with linear solver MUMPS 5.6.2.

Number of nonzeros in equality constraint Jacobian...: 109957
Number of nonzeros in inequality constraint Jacobian.: 4998
Number of nonzeros in Lagrangian Hessian.............: 112456

Total number of variables............................: 27495
                     variables with only lower bounds: 9996
                variables with lower and upper bounds: 4999
                     variables with only upper bounds: 0
Total number of equality constraints.................: 24995
Total number of inequality constraints...............: 2500
        inequality constraints with only lower bounds: 2500
   inequality constraints with lower and upper bounds: 0
        inequality constraints with only upper bounds: 0

```

I truncated the tail as before because it was simply far too long to fit

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [March 8, 2024, 7:03pm UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/18 "2024-03-08T19:03:34Z")

</div>

You must have changed something 😄

The larger problem is that Ipopt assumes the problem is convex. It can struggle to solve nonconvex problems ike this one. You should expect that relatively minor changes to the formulation can have big changes to the solution speed.

You should also take a look at [GitHub - infiniteopt/InfiniteOpt.jl: An intuitive modeling interface for infinite-dimensional optimization problems.](https://github.com/infiniteopt/InfiniteOpt.jl) which is intended for optimal control problems.

---

<div class="post-metadata">

**Author:** ![lpz18](https://avatars.discourse-cdn.com/v4/letter/l/ec9cab/32.png) [@lpz18](https://discourse.julialang.org/u/lpz18)\
**Post date:** [March 8, 2024, 8:00pm UTC](https://discourse.julialang.org/t/help-solving-adding-a-few-equations-to-ode-slows-jump-100x/111321/19 "2024-03-08T20:00:54Z")

</div>

ok, thanks!