On optimality conditions, minimizing and stationary sequences for nonsmooth functions

This thesis is devoted to study the optimization theory of non-smooth functions. The main body of the paper is divided into three parts. The first part studies the optimality conditions for semi-continuous functions. We present Theorem A. Let X be a Banach space with a Lipschitz ;Theorem B. Let X be a Banach space with a Lipschitz ;Theorem C. Let X be a Banach space. Let ;Theorem D. Let X be a Banach space and suppose that it admits a Lipschitz ;The last part we study algorithm methods for convex non-smooth functions in optimization problem. Three algorithm methods have been considered. We show mainly.;Theorem E. Assume ;In the same chapter, we also study constrained problems and obtain corresponding result.