Some Results In Nonsmooth Analysis And Optimization

Firstly, Fritz John conditions for quasi-differentiable functiongs with hybrid constraints are proposed in this paper. Sencondly, three theorems on properties of K'-convexificator of operator are presented. Lastly, based on basic principle of Fejer mapping, we construct Fejer Algorithm for solving a class of nonsmooth semi-infinite programming problems and prove its convergence.In Chapter 2, Fritz John conditions for quasi-differentiable functions with hybrid constraints are presented from the definitions of Polyakova regularity and Shapiro regularity.In Chapter 3,we first introduce two definitions of convexificator. Contraposing Jeyaku-mar and Luc convexificators,we define a regular convexificator. Then we construct unique minimum regular convexificator and minimum convexificator , moreover,some conditions for convexificator are given. At the last of the chapter, the basic definition of K'-convexificator of operator in general Banach space is investigated, and three theorems on properties of K'-covexificatoe of operator are presented.In Chaper 4,we first give some fundamental properties of Fejer mapping. And the based on the fundamental principle of Fejer mapping, Fejer Algorithm for solving a clars of nonsmooth semi-infinite programming problems is presented and prove its convergence.