A class of nonconvex semidefinite programming in which every KKT point is globally optimal

Abstract

We consider a special class of nonconvex semidefinite programming problems and show that every point satisfying the Karush--Kuhn--Tucker (KKT) conditions is globally optimal despite nonconvexity. This property is related to pseudoconvex optimization and fractional programming. We also present several applications to robust fractional programming and generalized eigenvalue optimization appearing in topology optimization, network control, finance, etc.