Approximation of optimization problems with constraints through kernel Sum-Of-Squares

arXiv:2301.06339v2 Announce Type: replace-cross
Abstract: Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through kernel Sum-Of-Squares (kSoS) approximations. We propose here a unified theorem to prove convergence guarantees for these schemes. Pointwise inequalities are turned into equalities within a class of nonnegative kSoS functions. Assuming further that the functions appearing in the problem are smooth, focusing on pointwise …

abstract approximation articles arxiv constraints convergence cs.lg fields global inequality kernel math.oc optimization prove spaces squares theorem through transport type