Can Manopt solve this optimization problem?

[David duan]

Thank you very much for the useful Manopt. Now I have a constraint optimization with both the Stiefel manifold constraint and the quadratic constraint. From example, the constraint is (aXb)^2<=c in which the a,b are vectors, c is scalar and X is the decision matrix. If it cannot be solved by Manopt, I wonder if you can tell me which optimization method can be used to solve it. Thank you very much!

[Nicolas Boumal]

Hello David,

Do you mean to say that X is on the Stiefel manifold, and a, b, c are also variables, or they are fixed?

In general, dealing with inequalities is not direct in manopt. If there are just a few, it sometimes works well to penalize for the inequalities in the cost function, instead of enforcing them directly.

I do not know which other toolbox to recommend for this type of problem. It would help to have a more precise statement of the problem.

Best,

Nicolas