Duality Theorems for Convex and Quasiconvex Set Functions

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 first topic is about quasiconjugates and polar sets. The second is about three types of set containment characterizations. The third is abou...

Lyapunov Functions and Duality for Convex Processes

The paper studies convex Lyapunov functions for differential and difference inclusions with right-hand sides given by convex processes, that is, by set-valued mappings the graphs of which are convex cones. Convex conjugacy between weak Lyapunov functions for such inclusions and Lyapunov functions for adjoint inclusions is established. Asymptotic stability concepts are compared and the existence...

WEAK AND STRONG DUALITY THEOREMS FOR FUZZY CONIC OPTIMIZATION PROBLEMS

The objective of this paper is to deal with the fuzzy conic program- ming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a speci c ordering cone is established based on the parameterized representation of fuzzy numbers. Un- der this setting, duality t...

Fenchel’s duality theorem for nearly convex functions

We present an extension of Fenchel’s duality theorem to nearly convexity, giving weaker conditions under which it takes place. Instead of minimizing the difference between a convex and a concave function, we minimize the subtraction of a nearly concave function from a nearly convex one. The assertion in the special case of Fenchel’s duality theorem that consists in minimizing the difference bet...

Hahn-Banach theorems for convex functions