Near-optimal solutions of convex semi-infinite programs via targeted sampling

We propose an approach to find the optimal value of a convex semi-infinite program (SIP) that involves identifying finite set relevant constraints by solving finite-dimensional global maximization problem. One major advantages our is it admits plug-and-play module where any suitable optimization algorithm can be employed obtain SIP. As example, we simulated annealing based which useful especially when constraint index high-dimensional. A proof convergence included, and performance accuracy itself are illustrated on several benchmark SIPs lifted from literature.