The UV-Decomposition's Theory And Application Of Proper Convex Funtion

Content:The UV-decomposition theory of a series of proper convex func-tion is mainly discussed in this paper. There are four chapters. Thefirst chapter is forward. We mainly introduce the background of theUV-decomposition. The second chapter is preliminary of knowledge.Firstly, we review the conceptions and the properties of the generalconvex sets and functions. Secondly, the conceptions and the proper-ties of the polyhedral convex sets and functions are given. At last,we review the UV-decomposition theory of the finite-value convexfunction. In chapter three, the UV-decomposition theory and the U-Lagrangian are provided for a series of proper convex function. Sincethe subdifferential of f at x∈rb(domf) is a unbounded set, wedefine a set which has the same function as the subdifferential set.Based on this set, we introduce the definition of the decomposition ofthe space,U-Lagrangian and its first-order and second-order devel-opment. In the last chapter, the UV-decomposition theory is appliedto the constrained programming.