Quasiconvex duality theorems with quasiconjugates and generator

This paper is based on the author's thesis, \On duality theorems for quasiconvex programming. In this paper, we investigate duality theorems for quasiconvex programming as generalizations of results in convex programming, and consists of three topics. The rst topic is about quasiconjugates and polar sets. The second is about three types of set containment characterizations. The third is about constraint qualications for Lagrange-type duality theorem in quasiconvex programming.