Semi definite programming and direct support for trace of matrix?

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  • Yuriy Zinchenko

    In its current form, no, but ...

    Although Gurobi does not implement barrier or any other algorithms for SDP, if you have a toy-sized SDP model, we can still do something with it starting from the upcoming release 9.0 (by the end of Nov 2019).  Note with 9.0 we allow non-convex quadratics, e.g., equality constraints like x^2 == y, which in turn permits building multi-variate polynomial constraints.  Now, in all the likelihood you will not be able to deal with polynomial-equality constraints for large degrees, however, for "small" matrices I would certainly try re-expressing SDP constraints as a set of, say, polynomial inequalities on determinants of the principal minors, e.g., see here, https://en.wikipedia.org/wiki/Sylvester%27s_criterion

    It may be worth a try, so hope it helps.

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