Semi-infinite Programming Problems with an Infinite Number of Conic Constraints and Algorithms for Solving Them

Abstract

The semi-infinite programming problem(SIP) is an optimization problem having an infinite number of inequality constrains and a finite number of variables. Since many important problems in the real world can be formulated in a natural manner as SIPs, many researchers have developed theories and algorithms for solving SIPs. In recent years, special SIPs involving infinitely many conic constraints (SICP) have been studied extensively because of its interesting structure and wide applications. In this paper, we introduce two algorithms for solving SICPs and observe their specific properties concerning global and local convergences.