Duality Theorems for Quasiconvex Programming with a Reverse Quasiconvex Constraint

Abstract

In this paper, we study duality theorems for quasiconvex programming with a reverse quasiconvex constraint. We introduce quasiaffine transformation methods for a reverse quasiconvex constraint. Especially, we show a linear characterization of a reverse quasiconvex constraint. By using transformation methods, we show necessary optimality conditions in terms of Greenberg-Pierskalla subdifferential. In addition, we introduce a surrogate duality theorem for quasiconvex programming with a reverse quasiconvex constraint.