A Type Of Generalized Convexity And Applications In Optimization Theory

This thesis,consisting of three chapters,discusses a type of generalized convexity and other related ones and their applications in optimization theory.In chapter 1,I point out the importance of convexity concept in optimization theory;At the same time, the process of investigating on generalized convexity and the applications in optimization theory is reviewed;In addition,I prove that the generalized convexity studied in this thesis is one of the most generalized kinds so far; Also included in this chapter is my demonstration of the rationality and the significance of the conditions and the definitions proposed by this thesis.Therefore, many conclusions included in the thesis cover the counterparts appearing in the former literature and are creative .In chapter 2,the criteria for semi-prequasi-invex functions and other related type functions are carefully investigated,respectively .The criteria generalize the counterparts appearing in the former literature such as some conclusions in the literature [2],[8].chapter 3,consisting of four sections,discusses the applications of semi-preinvex property to optimization theory.Section 3.1 deals with the optimal conditions.In this part,two fresh definitions-Definition3.1.1 and Definition3.1.2 are introduced.At the same time,by means of the assumption of semi-preinvex property ,employing these two definitions,the Fritz. John type optimal conditions and the Kuhn-Tucker type optimal conditions for the single-objective programming and the multi-objective programming are developed, respectively. Also included in this part is the saddle-point theory for the both types programmings. Especially,what i would like to propose is the conditions used to confirm the Kuhn-Tucker type optimal sufficient conditions...