Nonlinear expression without scalar expressions

Specific Domains Optimization (Mathematical)
1

Hi, I’ve read that nonlinear optimization has limited support. Unfortunately, my objective function cannot be written with scalar expressions and my matrix variable is at least 1000x1000 and I need to call several functions to build my objective function (the variable is a support function, that I need to differentiate, and construct a parametric function that I have to integrate…). The code required to compute aireSurface(h) or volumeSurface(h) has 200 lines.

My code is something like that

    model = Model(Ipopt.Optimizer)
    register(model, :aireSurface, 1, aireSurface; autodiff = true)
    set_optimizer_attribute(model, "print_level", 1)
    @variables(
        model,
        begin
        h[1:N,1:M]<=b/2.0
        end
    )
    @NLobjective( 
        model,
        Max,
        aireSurface(h)
    )
    @constraint(
        # convexity
        model,
        convexity(h) .>= 0
    )
    @constraint(
        # volume
        model,
        volumeSurface(h) == lambdaI*4.0/3.0*pi*((b/2.0)^3),
    )

Is there any workaround to do that ? Thanks

2

No, there is no work-around for JuMP.

You might want to try Nonconvex.jl instead: Getting started · Nonconvex.jl

3

But I will say, you have a black-box function with 1,000,000 variables. That’s going to be challenging to solve. Have you considered alternative approaches?