Abstract
In this article, we are concerned with a nondifferentiable minimax fractional programming problem. We derive the sufficient condition for an optimal solution to the problem and then establish weak, strong, and strict converse duality theorems for the problem and its dual problem under B-(p, r)-invexity assumptions. Examples are given to show that B-(p, r)-invex functions are generalization of (p, r)-invex and convex functions AMS Subject Classification: 90C32; 90C46; 49J35.
Highlights
1 Introduction The mathematical programming problem in which the objective function is a ratio of two numerical functions is called a fractional programming problem
Fractional programming problems have arisen in multiobjective programming [1,2], game theory [3], and goal programming [4]
The necessary and sufficient conditions for generalized minimax programming were first developed by Schmitendorf [5]
Summary
The mathematical programming problem in which the objective function is a ratio of two numerical functions is called a fractional programming problem. Tanimoto [6] applied these optimality conditions to define a dual problem and derived duality theorems.
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