JuMP register function

Specific Domains Optimization (Mathematical)
1

Hello,
This is my first time using JuMP hence my question is basic.

The following fails

using JuMP, Ipopt

f(x) = x[1]^2 + x[2]^2
∇f(x) = [2*x[1], 2*x[2]]
∇²f(x) = [2 0; 0 2]
model = Model(Ipopt.Optimizer)
register(model, :my_fun, 1, f,∇f, ∇²f)
lb = [-1.0, -1.0]
ub = [1.0, 1.0]
@variable(model, lb[i] <= x[i=1:2] <= ub[i])
@NLobjective(model, Min, my_fun(x))
JuMP.optimize!(model)

with the error:

ERROR: LoadError: Unexpected array VariableRef[x[1], x[2]] in nonlinear expression. Nonlinear expressions may contain only scalar expressions.

The same occurs if I define the function as:

function my_function(x::T...) where {T<:Real}
    y = zeros(T, length(x))
    for i in eachindex(y)
        y[i] = x[i]^2
    end
    return sum(y)
end

I do not know why this occurs.
Any help is appreciated.

2

Hi @Sushrut_Deshpande, welcome to JuMP!

See the documentation: Nonlinear Modeling · JuMP

The correct syntax is:

julia> using JuMP, Ipopt

julia> f(x...) = x[1]^2 + x[2]^2
f (generic function with 1 method)

julia> function ∇f(g, x...)
           g[1] = 2*x[1]
           g[2] = 2*x[2]
       end
∇f (generic function with 1 method)

julia> function ∇²f(H, x...)
           H[1, 1] = 2.0
           H[2, 2] = 2.0
       end
∇²f (generic function with 1 method)

julia> model = Model(Ipopt.Optimizer)
A JuMP Model
├ solver: Ipopt
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> @operator(model, op_fun, 2, f, ∇f, ∇²f)
NonlinearOperator(f, :op_fun)

julia> lb = [-1.0, -1.0]
2-element Vector{Float64}:
 -1.0
 -1.0

julia> ub = [1.0, 1.0]
2-element Vector{Float64}:
 1.0
 1.0

julia> @variable(model, lb[i] <= x[i in 1:2] <= ub[i])
2-element Vector{VariableRef}:
 x[1]
 x[2]

julia> @objective(model, Min, op_fun(x...))
op_fun(x[1], x[2])

julia> optimize!(model)

******************************************************************************
This program contains Ipopt, a library for large-scale nonlinear optimization.
 Ipopt is released as open source code under the Eclipse Public License (EPL).
         For more information visit https://github.com/coin-or/Ipopt
******************************************************************************

This is Ipopt version 3.14.17, running with linear solver MUMPS 5.7.3.

Number of nonzeros in equality constraint Jacobian...:        0
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        3

Total number of variables............................:        2
                     variables with only lower bounds:        0
                variables with lower and upper bounds:        2
                     variables with only upper bounds:        0
Total number of equality constraints.................:        0
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   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  0.0000000e+00 0.00e+00 0.00e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  0.0000000e+00 0.00e+00 0.00e+00  -1.7 0.00e+00    -  1.00e+00 1.00e+00   0
   2  0.0000000e+00 0.00e+00 0.00e+00  -3.8 0.00e+00    -  1.00e+00 1.00e+00T  0
   3  0.0000000e+00 0.00e+00 0.00e+00  -5.7 0.00e+00    -  1.00e+00 1.00e+00T  0
   4  0.0000000e+00 0.00e+00 0.00e+00  -8.6 0.00e+00    -  1.00e+00 1.00e+00T  0

Number of Iterations....: 4

                                   (scaled)                 (unscaled)
Objective...............:   0.0000000000000000e+00    0.0000000000000000e+00
Dual infeasibility......:   0.0000000000000000e+00    0.0000000000000000e+00
Constraint violation....:   0.0000000000000000e+00    0.0000000000000000e+00
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   2.5059035596800808e-09    2.5059035596800808e-09
Overall NLP error.......:   2.5059035596800808e-09    2.5059035596800808e-09


Number of objective function evaluations             = 5
Number of objective gradient evaluations             = 5
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 4
Total seconds in IPOPT                               = 1.762

EXIT: Optimal Solution Found.

But if function tracing works, you can do:

using JuMP, Ipopt
f(x...) = x[1]^2 + x[2]^2
model = Model(Ipopt.Optimizer)
lb = [-1.0, -1.0]
ub = [1.0, 1.0]
@variable(model, lb[i] <= x[i in 1:2] <= ub[i])
@objective(model, Min, my_fun(x...))
optimize!(model)

but even simpler, you can do:

using JuMP, Ipopt
model = Model(Ipopt.Optimizer);
@variable(model, -1 <= x[i in 1:2] <= 1)
@objective(model, Min, x[1]^2 + x[2]^2)
optimize!(model)
3

Hello,
Thank you for the answer.
I have just 1 small question now:
What would be the difference between using @operator and register, the syntax seems to be same.

by intuition wouldn’t I register a custom function?

4

See ANN: JuMP v1.15 is released

register is the old syntax.

5

thank you

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