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Published 20 hours ago • verified publisher icon jump-dev

Support SumOfSquares MOI extension

Open blegat opened this issue 6 years ago • 2 comments

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.

blegat avatar Jul 11 '19 15:07 blegat

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.

chriscoey avatar Jul 29 '19 19:07 chriscoey

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.

lkapelevich avatar Jan 20 '20 19:01 lkapelevich