OPTIMIZATION THEORY FOR SET FUNCTIONS IN NONDIFFERENTIABLE FRACTIONAL PROGRAMMING WITH MIXED TYPE DUALITY

Abstract

We revisit optimization theory involving set functions which are defined on a family of measurable subsets in a measure space. In this paper, we focus on a minimax fractional programming problem with subdifferentiable set functions. Using nonparametric necessary optimality conditions, we introduce generalized $(\mathcal{F},\rho, \theta)$-convexity to establish several sufficient optimality conditions for a minimax programming problem, and construct a new dual model to unify the Wolfe type dual and the Mond-Weir type dual as special cases of this dual programming problem. Finally we establish a weak, strong, and strict converse duality theorem.