# JuMP model warm start using Ipopt

**URL:** <https://discourse.julialang.org/t/jump-model-warm-start-using-ipopt/92660>\
**Category:** Optimization (Mathematical)\
**Tags:** question, jump, ipopt\
**Created:** [January 8, 2023, 9:46am UTC](https://discourse.julialang.org/t/jump-model-warm-start-using-ipopt/92660 "2023-01-08T09:46:14Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![Xuekui\_wang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xuekui_wang/32/30746_2.png) [@Xuekui\_wang](https://discourse.julialang.org/u/Xuekui_wang)\
**Post date:** [January 8, 2023, 9:46am UTC](https://discourse.julialang.org/t/jump-model-warm-start-using-ipopt/92660/1 "2023-01-08T09:46:14Z")

</div>

I am solving a non-convex problem using Ipopt, and I want to warm start the same problem.  
That not only needs to set start variable value using`set_start_value`, but also needs to set duals and multipliers.  
How can I access all duals and multipliers and input them to the model?

```julia
set_optimizer(model, Ipopt.Optimizer)
optimize!(model)

```

There is a function `set_optimal_start_values `In JuMP document, but it can not be used with Ipopt.

```julia
function set_optimal_start_values(model::Model)
    # Store a mapping of the variable primal solution
    variable_primal = Dict(x => value(x) for x in all_variables(model))
    # In the following, we loop through every constraint and store a mapping
    # from the constraint index to a tuple containing the primal and dual
    # solutions.
    constraint_solution = Dict()
    for (F, S) in list_of_constraint_types(model)
        # We add a try-catch here because some constraint types might not
        # support getting the primal or dual solution.
        try
            for ci in all_constraints(model, F, S)
                constraint_solution[ci] = (value(ci), dual(ci))
            end
        catch
            @info("Something went wrong getting $F-in-$S. Skipping")
        end
    end
    # Now we can loop through our cached solutions and set the starting values.
    for (x, primal_start) in variable_primal
        set_start_value(x, primal_start)
    end
    for (ci, (primal_start, dual_start)) in constraint_solution
        set_start_value(ci, primal_start)
        set_dual_start_value(ci, dual_start)
    end
    return
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:** [January 8, 2023, 10:06pm UTC](https://discourse.julialang.org/t/jump-model-warm-start-using-ipopt/92660/2 "2023-01-08T22:06:41Z")

</div>

It looks like setting the constraint primal isn’t supported by Ipopt yet. Just comment out that line. I also added a line to set the dual of the nonlinear constraints.

```julia
julia> using JuMP, Ipopt

julia> function set_optimal_start_values(model::Model)
           # Store a mapping of the variable primal solution
           variable_primal = Dict(x => value(x) for x in all_variables(model))
           # In the following, we loop through every constraint and store a mapping
           # from the constraint index to a tuple containing the primal and dual
           # solutions.
           constraint_solution = Dict()
           nlp_dual_start = nonlinear_dual_start_value(model)
           for (F, S) in list_of_constraint_types(model)
               # We add a try-catch here because some constraint types might not
               # support getting the primal or dual solution.
               try
                   for ci in all_constraints(model, F, S)
                       constraint_solution[ci] = (value(ci), dual(ci))
                   end
               catch
                   @info("Something went wrong getting $F-in-$S. Skipping")
               end
           end
           # Now we can loop through our cached solutions and set the starting values.
           for (x, primal_start) in variable_primal
               set_start_value(x, primal_start)
           end
           for (ci, (primal_start, dual_start)) in constraint_solution
               # set_start_value(ci, primal_start)
               set_dual_start_value(ci, dual_start)
           end
           set_nonlinear_dual_start_value(model, nlp_dual_start)
           return
       end
set_optimal_start_values (generic function with 1 method)

julia> model = Model(Ipopt.Optimizer)
A JuMP Model
Feasibility problem with:
Variables: 0
Model mode: AUTOMATIC
CachingOptimizer state: EMPTY_OPTIMIZER
Solver name: Ipopt

julia> @variable(model, x >= 0)
x

julia> @NLconstraint(model, x^2 <= 1)
x ^ 2.0 - 1.0 ≤ 0

julia> @objective(model, Max, x)
x

julia> optimize!(model)
This is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 1
Number of nonzeros in Lagrangian Hessian.............: 1

Total number of variables............................: 1
                     variables with only lower bounds: 1
                variables with lower and upper bounds: 0
                     variables with only upper bounds: 0
Total number of equality constraints.................: 0
Total number of inequality constraints...............: 1
        inequality constraints with only lower bounds: 0
   inequality constraints with lower and upper bounds: 0
        inequality constraints with only upper bounds: 1

iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
   0 9.9999900e-03 0.00e+00 1.98e+00 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
   1 1.1773946e-01 0.00e+00 9.86e-01 -1.0 1.08e-01 - 5.58e-01 1.00e+00f 1
   2 3.7890821e+00 1.34e+01 2.47e+00 -1.7 3.67e+00 - 6.52e-02 1.00e+00f 1
   3 2.0163545e+00 3.07e+00 3.94e-01 -1.7 1.77e+00 - 1.00e+00 1.00e+00h 1
   4 1.2438830e+00 5.47e-01 5.70e-02 -1.7 7.72e-01 - 1.00e+00 1.00e+00h 1
   5 1.0080550e+00 1.62e-02 4.63e-02 -1.7 2.36e-01 - 1.00e+00 1.00e+00h 1
   6 9.9794206e-01 0.00e+00 4.09e-04 -2.5 3.52e-02 - 1.00e+00 1.00e+00h 1
   7 9.9984294e-01 0.00e+00 8.28e-06 -3.8 3.90e-03 - 1.00e+00 1.00e+00h 1
   8 9.9999813e-01 0.00e+00 4.51e-08 -5.7 3.14e-04 - 1.00e+00 1.00e+00h 1
   9 1.0000000e+00 0.00e+00 6.87e-12 -8.6 3.78e-06 - 1.00e+00 1.00e+00h 1

Number of Iterations....: 9

                                   (scaled) (unscaled)
Objective...............: -1.0000000024889628e+00 1.0000000024889628e+00
Dual infeasibility......: 6.8741856104894100e-12 6.8741856104894100e-12
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 2.5127966495526885e-09 2.5127966495526885e-09
Overall NLP error.......: 2.5127966495526885e-09 2.5127966495526885e-09

Number of objective function evaluations = 10
Number of objective gradient evaluations = 10
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 10
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 10
Number of Lagrangian Hessian evaluations = 9
Total seconds in IPOPT = 0.004

EXIT: Optimal Solution Found.

julia> set_optimal_start_values(model)

julia> optimize!(model)
This is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 1
Number of nonzeros in Lagrangian Hessian.............: 1

Total number of variables............................: 1
                     variables with only lower bounds: 1
                variables with lower and upper bounds: 0
                     variables with only upper bounds: 0
Total number of equality constraints.................: 0
Total number of inequality constraints...............: 1
        inequality constraints with only lower bounds: 0
   inequality constraints with lower and upper bounds: 0
        inequality constraints with only upper bounds: 1

iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
   0 1.0000000e+00 0.00e+00 1.99e-09 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
   1 9.8764269e-01 0.00e+00 1.17e-02 -1.7 1.47e-02 - 1.00e+00 1.00e+00h 1
   2 9.9675597e-01 0.00e+00 4.71e-04 -2.5 1.82e-02 - 1.00e+00 1.00e+00h 1
   3 9.9983859e-01 0.00e+00 1.56e-05 -3.8 6.23e-03 - 1.00e+00 1.00e+00h 1
   4 9.9999813e-01 0.00e+00 4.55e-08 -5.7 3.29e-04 - 1.00e+00 1.00e+00h 1
   5 1.0000000e+00 0.00e+00 6.88e-12 -8.6 3.78e-06 - 1.00e+00 1.00e+00h 1

Number of Iterations....: 5

                                   (scaled) (unscaled)
Objective...............: -1.0000000024889595e+00 1.0000000024889595e+00
Dual infeasibility......: 6.8763058686346261e-12 6.8763058686346261e-12
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 2.5128010673512823e-09 2.5128010673512823e-09
Overall NLP error.......: 2.5128010673512823e-09 2.5128010673512823e-09

Number of objective function evaluations = 6
Number of objective gradient evaluations = 6
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 6
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 6
Number of Lagrangian Hessian evaluations = 5
Total seconds in IPOPT = 0.005

EXIT: Optimal Solution Found.

```

---

<div class="post-metadata">

**Author:** ![Xuekui\_wang](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/xuekui_wang/32/30746_2.png) [@Xuekui\_wang](https://discourse.julialang.org/u/Xuekui_wang)\
**Post date:** [January 9, 2023, 5:01am UTC](https://discourse.julialang.org/t/jump-model-warm-start-using-ipopt/92660/3 "2023-01-09T05:01:49Z")

</div>

Thank you @odow ， it is a great help for me.  
Does it mean setting the constraint primals is not useful for Ipopt?  
I solve your model by two steps: the first is to get all primal and dual values of variables and constraints.  
Second, set all primal values and dual values, then `set_optimizer(model, Ipopt.Optimizer)` and `optimize!(model)`.  
The result is also 5 iterations.

```julia
function var_value(model::Model, constraint_solution::Dict, solution::Bool=true)
    for (F, S) in list_of_constraint_types(model)
        # We add a try-catch here because some constraint types might not
        # support getting the primal or dual solution.
        try
            if solution
                for ci in all_constraints(model, F, S)
                    constraint_solution[ci] = (value(ci), dual(ci))
                end
            else
                for ci in all_constraints(model, F, S)
                    constraint_solution[ci] =0.0
                end
            end
        catch
            @info("Something went wrong getting $F-in-$S. Skipping")
        end
    end
    return constraint_solution
end

```

```julia
variable_primal = Dict(string(x)=> value(x) for x in all_variables(model))
constraint_solution = Dict()
var_value(model, constraint_solution, true)
constraint_solution = Dict(string(x) =>(i,j) for (x,(i,j)) in constraint_solution)

model1 = Model()
@variable(model1, x>=0)
@NLconstraint(model1, x^2<=1)
@objective(model1, Max, x)

variable_start = Dict(x => start_value(x) for x in all_variables(model1))
constraint_solution_nopt = Dict()
var_value(model1, constraint_solution_nopt, false)

for (x, primal_start) in variable_start
    set_start_value(x, variable_primal[string(x)])
end
for (ci, x) in constraint_solution_nopt
    set_start_value(ci, constraint_solution[string(ci)][1])
    set_dual_start_value(ci, constraint_solution[string(ci)][2])
end

# nlp_dual_start = nonlinear_dual_start_value(model)
nlp_dual_start_opt = dual.(all_nonlinear_constraints(model))
set_nonlinear_dual_start_value(model1, nlp_dual_start_opt)

set_optimizer(model1, Ipopt.Optimizer)
optimize!(model1)

```

```julia
This is Ipopt version 3.14.4, running with linear solver MUMPS 5.4.1.

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 1
Number of nonzeros in Lagrangian Hessian.............: 1

Total number of variables............................: 1
                     variables with only lower bounds: 1
                variables with lower and upper bounds: 0
                     variables with only upper bounds: 0
Total number of equality constraints.................: 0
Total number of inequality constraints...............: 1
        inequality constraints with only lower bounds: 0
   inequality constraints with lower and upper bounds: 0
        inequality constraints with only upper bounds: 1

iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
   0 1.0000000e+00 0.00e+00 1.99e-09 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
   1 9.8764269e-01 0.00e+00 1.17e-02 -1.7 1.47e-02 - 1.00e+00 1.00e+00h 1
   2 9.9675597e-01 0.00e+00 4.71e-04 -2.5 1.82e-02 - 1.00e+00 1.00e+00h 1
   3 9.9983859e-01 0.00e+00 1.56e-05 -3.8 6.23e-03 - 1.00e+00 1.00e+00h 1
   4 9.9999813e-01 0.00e+00 4.55e-08 -5.7 3.29e-04 - 1.00e+00 1.00e+00h 1
   5 1.0000000e+00 0.00e+00 6.88e-12 -8.6 3.78e-06 - 1.00e+00 1.00e+00h 1

Number of Iterations....: 5

                                   (scaled) (unscaled)
Objective...............: -1.0000000024889595e+00 1.0000000024889595e+00
Dual infeasibility......: 6.8763058686346261e-12 6.8763058686346261e-12
Constraint violation....: 0.0000000000000000e+00 0.0000000000000000e+00
Variable bound violation: 0.0000000000000000e+00 0.0000000000000000e+00
Complementarity.........: 2.5128010673512823e-09 2.5128010673512823e-09
Overall NLP error.......: 2.5128010673512823e-09 2.5128010673512823e-09

Number of objective function evaluations = 6
Number of objective gradient evaluations = 6
Number of equality constraint evaluations = 0
Number of inequality constraint evaluations = 6
Number of equality constraint Jacobian evaluations = 0
Number of inequality constraint Jacobian evaluations = 6
Number of Lagrangian Hessian evaluations = 5
Total seconds in IPOPT = 0.077

EXIT: Optimal Solution Found.

```