How can i use sets created using LasySets.jl with Convex.jl variables?

Specific Domains
1

Is there a way i can create LazySets Polyhedron and use it as a variable in my optimization program that uses Convex.jl, use them in constraints i want to add to the problem?.

2

I don’t think there’s any interoperability already set up for those two packages. I think you can use Polyhedra.jl to create a constraint for JuMP.jl, however: http://juliapolyhedra.github.io/Polyhedra.jl/stable/optimization/#Polyhedra.linear_objective_solver.

3

Thanks.

4

Hi @adropintheriver,

Integration of LazySets.jl types with JuMP is implemented in the package InvariantSets.jl (thanks to @uweschler). We should probably refactor that conversion code to LazySets.jl and make it available when users load JuMP.

With respecto to Convex.jl I’m not aware of such conversions but I guess it shouldn’t be too hard
(PRs welcome).

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5

Nice! If InvariantSets.jl worked on the MathOptInterface (MOI) level instead of the JuMP level, then support for Convex should be even easier (since both Convex and JuMP are MOI frontends). MOI can be a bit harder to work with than JuMP though so maybe it’s not worth it.

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6

Do you have a use case or MWE of the kind of problem you want to address?

Note that constraints can be added easily in this way:

using LazySets, Convex, SCS

function Convex.add_constraint!(x::Convex.AbstractVariable, X::LazySet)
    A, b = tosimplehrep(X)
    add_constraint!(x, A*x ≤ b)
end

Example use:

function supfunc(d::AbstractVector, X::LazySet; solver=SCS.Optimizer(verbose=false))
    x = Variable(length(d))
    add_constraint!(x, X) # x ∈ X
    xᵀd = dot(x, d)
    solve!(maximize(xᵀd), solver)
    return evaluate(xᵀd)
end

X = rand(VPolygon)
d = ones(2)

supfunc(d, X) ≈ ρ(d, X)  # ρ is defined on LazySets for each set / lazy operation
true
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8

hi @mforets, yes, i have tried to describe the use-case here 3D bin packaging using Convex.jl