Computation Algorithm for Convex Semi-infinite Program with Second-Order Cones: Special Analyses for Affine and Quadratic Case

Abstract

We focus on the convex semi-infinite program with second-order cone constraints (for short, SOCCSIP), which has wide applications such as filter design, robust optimization, and so on. For solving the SOCCSIP, we propose an explicit exchange method, and prove that the algorithm terminates in a finite number of iterations. In the convergence analysis, we do not need to use the special structure of second-order cone (SOC) when the objective or constraint function is strictly convex. However, if both of them are non-strictly convex and constraint function is affine or quadratic, then we have to utilize the SOC complementarity conditions and the spectral factorization techniques associated with Euclidean Jordan algebra. We also show that the obtained output is an approximate optimum of SOCCSIP. We report some numerical results involving the application to the robust optimization in the classical convex semi-infinite program.