How to add user-defined nonlinear functions as constraints with JuMP?

Specific Domains Optimization (Mathematical)
1

Is it possible to add user-defined nonlinear functions as constraints in JuMP? I couldn’t find any documentation about a case like this nor any examples where someone would have done this.
I mean something like this:

JuMP.register(m, :g, 1, g, autodiff=true)
JuMP.addNLconstraint(m, g(x) <= 0)

If this is not possible, then is there any way to do this kind of optimization with Julia?

2

Have you tried? It should work exactly as you have :slight_smile: (Although you probably want to use @NLconstraint instead of addNLconstraint.)

The docs are being updated for the new version of JuMP, but I have opened an issue to make sure it gets addressed. https://github.com/JuliaOpt/JuMP.jl/issues/1323

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3

Yes of course I’ve tried my example @odow , but it didn’t work, probably because my variable was a vector. However I now figured how it can be done:

f(x) = x[1]^2+2*x[2]+3
g(x) = x[1]^3+x[2]^2

JuMP.register(m, :f, 2, f, autodiff=true)
JuMP.register(m, :g, 2, g, autodiff=true)

JuMP.setNLobjective(m, :Min, :(f($(x...)))
JuMP.addNLconstraint(m, :(g($(x...))<=10))) # This line is the one I had trouble with

Interesting that similar examples really don’t exist anywhere in JuMP’s documentation.

4

Yes of course I’ve tried my example

Oops, sorry for coming across as blunt, it wasn’t clear if it was a general question or whether there was a specific problem.

Glad you got it working. Another option is:

using JuMP, Ipopt

m=Model(solver=IpoptSolver())
@variable(m, x[1:2])

f(x...) = x[1]^2+2*x[2]+3
g(x...) = x[1]^3+x[2]^2

JuMP.register(m, :f, 2, f, autodiff=true)
JuMP.register(m, :g, 2, g, autodiff=true)

@NLobjective(m, Min, f(x[1], x[2]))
@NLconstraint(m, g(x[1], x[2]) <= 10)

solve(m)

Interesting that similar examples really don’t exist anywhere in JuMP’s documentation.

Yes. Pull requests to improve the docs are always welcome :slight_smile:

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