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jump-dev / Hypatia.jl

interior point solver for general convex conic optimization problems
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Support SumOfSquares MOI extension #283

Open blegat opened 5 years ago

blegat commented 5 years ago

Hypatia should support the SOSPolynomialSet set: https://github.com/JuliaOpt/SumOfSquares.jl/blob/master/src/sos_polynomial.jl#L16-L29 so that when using the Hypatia solver with SumOfSquares, the PSD reformulation is not done.

chriscoey commented 5 years ago

as recently discussed with @blegat and @tweisser, we currently only support an interpolant-basis WSOS cone, which has a slightly more complicated parametrization than the cones currently defined by SumOfSquares. but it sounds like with the MultivariateBases.jl package, we may be able to move the interpolation code from ModelUtilities into there, and have an interpolant-basis cone defined there, which would make it trivial to use Hypatia from SumOfSquares.

lkapelevich commented 4 years ago

Just dropping info, when the domain includes equality constraints our set is no longer a proper cone (it's not pointed). To use the WSOS dual cone already defined in Hypatia we would need to either add additional constraints if formulating the moment problem or additional variables if formulating the polynomial problem.