An Explicit Exchange Algorithm For Linear Semi-Infinite Programming Problems With Second-Order Cone Constraints

In this paper, we propose an explicit exchange algorithm for solving semiinfinite programming problem (SIP) with second-order cone (SOC) constraints. We prove, by using the slackness complementarity conditions, that the algorithm terminates in a finite number of iterations and the obtained solution sufficiently approximates the original SIP solution. In existing studies on SIPs, only the nonnegative constraints were considered, and hence, the slackness complementarity conditions were separable to each component. However, in our study, the existing componentwise analyses are not applicable anymore since the slackness complementarity conditions are associated with SOCs. In order to overcome such a difficulty, we introduce a certain coordinate system based on the spectral factorization. In the numerical experiments, we solve some test problems to see the effectiveness of the proposed algorithm.