Integer optimisation with user's multivariate functions: Possible in Julia?

Specific Domains Optimization (Mathematical)
,
1

My optimisation problem has convex multivariate constraints with matrix operations: inverse and determinant. The matrices are symmetric PSD from dim 2x2 up to 10x10. I’ve solved the continuous case in JuMP and Ipopt, with user-defined multivariate constraints and analytical derivatives. This worked extremely well.

There’s been less luck with the integer case. What I’ve tried:

  • Define @NLconstraints in JuMP => The det and inv weren’t recognised

  • Use Pavito.jl and Ipopt with CbcSolver or CplexSolver => Requires Hessians, which isn’t possible in JuMP for multivariate user-defined functions, even though Ipopt doesn’t require exact Hessians

  • Juniper, POD, AmplNLWriter => No user-defined multivariate functions (to the best of my knowledge)

  • Convex.jl and SCS + Pajarito => some luck with the det, but slow convergence and inexact solutions, like -0.2039 for an Int x >= 0. Also, inv isn’t really allowed.

I’d very much appreciate any suggestions and recommendations of library tools, ideally open source. Many thanks!

2 Likes
2

If you have a JuMP model that is working for an NLP problem, I don’t foresee why Juniper would not work for an MINLP variant of that JuMP model. Can you indicate what type of error you are getting in that case?

3

I get “LoadError: KeyError: key :g not found”. Here, :g is the user-defined constraint registered with JuMP and added through JuMP.addNLconstraint. This constraint is indexed and added in a loop, as in JuMP; Rewriting an @eval @NLexpression with a user defined function in local scope w/ Expr

4

Can you provide me a small test script that I can work with?

1 Like
5

I found a workaround by disabling Hessians in Pavito if they aren’t provided by the JuMP model. There’s a PR in Disable Hessians when not provided by JuMP by spockoyno · Pull Request #12 · jump-dev/Pavito.jl · GitHub.

6

I’ve found a workaround, but maybe there’s a better solution. There’s an example script in my other question, How to avoid re-computing the same matrix in optimisation/JuMP? Many thanks!

7

@Olegg, glad to hear that you found a work around for Pavito.

Still, it would be a great help to us if you could provide a small JuMP model that exhibits this issue, then we can add it to the unit tests for various solvers to make sure they work for user defined functions.

8

Sure! I’ve edited and double-checked the code linked in my reply to @Wikunia. Should be working now with the workaround. Hope it helps.

9

@Olegg: I may have a similar problem here where I want to define constraints in JuMP involving matrix invs. Would you mind sharing how you registered a multivariate function / derivative? Or did you find an alternative approach?