Redundant Inequality constraints in moment model

[Philipp Spee]

Dear Professor Löfberg, 

I have a question about the implementation of Laserre's Moment hierarchy in the moment solver of Yalmip: When applying the relaxation to a problem the "standard procedure" is adding moment constraints and redundant equality constraints, and representing inequality constraints via localizing matrices (if I got everything right, I am not an expert). In this paper https://arxiv.org/abs/2208.10521 the author mentions additional redundant inequality constraints which can further tighten the relaxations but are not part of the standart procedure. (Appendix A, last paragraph). I wanted to ask if these constraints are implemented in yalmips moment solver.

Thank you in advance!

Kind regards, Philipp Spee

P.S. Thank you for saving me much time!

[Johan Löfberg]

If you have, say, the constraint x == 1, you will automatically have relaxations of the constraints such as x^2 == x in the model, if that is what you are asking. That happens when the equality constraint essentially is multiplied with the localizer matrix and then relaxed.

[Philipp Spee]

Thanks for the quick reply! I think my question was not clear: I was asking about inequalities. Normally you multiply one inequality, say g_i, with a moment matrix (of corresponding degree) to get the localizing matrix corresponding to the inequality g_i. In the paper the author talks about additionally building localizing matrices by multiplying inequalities, say g_i*g_j and then multiplying with a moment matrix. Is this also done in the moment solver?

[Johan Löfberg]

If you want to add redundant constraints from products of (in)equalities, you have to add those manually. 

[Philipp Spee]

Ok, thank you!