Parametric Duality Models For Semi-Infinite Fractional Programming Problems Involving Semi-E-Convex Functions

A semi-infinite programming problem is a mathematical programmingwith a finite number of variables and infinitely many constraints. Dualitytheories and generalized convexity concepts are important research topicsin mathematical programming.In this paper, we introduce some definition for semi-E-convex, quasi-semi-E-convex and pseudo-semi-E-convex and discuss their basic proper-ties, and establish some optimality conditions for a fractional programminginvolving semi-E-convex and related functions. These optimality criteria areutilized as a basic for constructing parametric dual model I and other para-metric dual model II (Wolfe type dual, Mond-Weir type dual and a mixedtype dual which unified the Wolfe type dual and Mond-Weir type) undersemi-E-convex functions. Furthermore, we establish three duality theorems:weak duality, strong duality and strict converse duality theorems,and provethat optimal values of the primal problem.This paper contains six chapters. We introduced significance of the sub-ject, research present situation and the content of the paper in the firstchapter; In chapter II, we present some function's basic knowledge andsome optimality conditions for a fractional programming; In chapter III;we construct dual model I and establish three duality theorems: weak dual-ity, strong duality and strict converse duality theorems; In chapter IV, weconstruct dual model II and establish three duality theorems: weak duality,strong duality and converse duality; In chapter V, we remark for furtherdevelopment. We make a summary of the full text in the last chapter.