Polynomial Optimization Relaxations for Generalized Semi-Infinite Programming
We study generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions. Moment-SOS relaxations are applied to solve the polynomial optimization. The convergence of this hierarchy is shown under certain conditions. In particular, the classical semi-infinite programs (SIPs) can be solved as a special case of GSIPs. We also study GSIPs that have convex infinity constraints and show that they can be solved exactly by a single polynomial optimization relaxation. The computational efficiency is demonstrated by extensive numerical results.
Tuesday, April 11, 2023
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9056