Duality for minimax fractional programming problems

Abstract

The work being presented in the present thesis is devoted to the study of duality results for minimax fractional programming problems under exponential (p; r)-invexity assumptions. The chapterwise summary of the thesis is as follows: Chapter 1 is introductory in nature. This chapter includes minimax fractional program- ming problem, de nitions, notations that are used throughout the work and detailed review of minimax fractional programming problems and summary of the thesis has also been discussed. In Chapter 2, we have studied a minimax fractional programming problem involving ex- ponential (p; r)-invex functions [16] and weak, strong and strict converse duality theorems are established under exponential (p; r)ô invex assumptions. In Chapter 3, we have reviewed a mixed-type dual problem with exponential (p; r)-invexity considered by Lai and Ho [12] and proved the duality theorems related to the primal problem and the mixed-type dual problem. In Chapter 4, motivated by Lai and Ho [10], we have established nonparametric necessary and su cient optimality conditions for a minimax fractional programming problem with B- (p; r)-invexity. These optimality conditions are deduced to two parameter-free type dual models: Mond-Weir type dual and Wolfe type dual problems. On these duality types, we have established the duality theorems under exponential B-(p; r) invexities including weak duality, strong duality and strict converse duality theorems.