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In this paper, we consider a nonlinear semi-infinite program that minimizes afunction including a log-determinant (logdet) function over positive definitematrix constraints and infinitely many convex inequality constraints, calledSIPLOG for short. The main purpose of the paper is to develop an algorithm forcomputing a Karush-Kuhn-Tucker (KKT) point for the SIPLOG efficiently. Morespecifically, we propose an interior point sequential quadraticprogramming-type method that inexactly solves a sequence of semi-infinitequadratic programs approximating the SIPLOG. Furthermore, to generate a searchdirection in the dual matrix space associated with the semi-definiteconstraint, we solve scaled Newton equations {that yield} the family ofMonteiro-Zhang directions. We prove that the proposed method weakly* convergesto a KKT point under some mild assumptions. Finally, we conduct some numericalexperiments to demonstrate the efficiency of the proposed method.

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