An interior point sequential quadratic programming-type method for log-determinant semi-infinite programs

摘要

In this paper, we consider a nonlinear semi-infinite program that minimizes a function including a log-determinant (logdet) function over positive definite matrix constraints and infinitely many convex inequality constraints. We call this problem SIPLOG, where SIP stands for Semi-Infinite Program and LOG comes from LOG-det function. The main purpose of the paper is to develop an algorithm for efficiently computing a Karush-Kuhn-Tucker (KKT) point for the SIPLOG. More specifically, we propose an interior point sequential quadratic programming-type method that solves inexactly a sequence of semi-infinite quadratic programs approximating the SIPLOG. Furthermore, to generate a search direction in the dual matrix space associated with the semi-definite constraint, we solve scaled Newton equations that yield the family of Monteiro-Zhang directions. We prove that the proposed method weakly* converges to a KKT point under some mild assumptions. Finally, we conduct some numerical experiments to demonstrate the efficiency of the proposed method. (C) 2020 Elsevier B.V. All rights reserved.