Recession Cones, Recession Functions And Characteristic Of Functions

In the optimized question research, objective function's condition has decided in the solution of the question that is existence or not , recession cones and recession function's related result has provided the effective tool for the function condition's portray. In this article,we first introduce the conception of recession cone and recession function in convex analysis written by Rockafellar and Feng deixing,so we obtain some corresponding conclusions about the existence of this minimal value on constraint set and unconstraint set. We are discuss two main parts in this paper , In the first part contains two chapters, and the propositions of recession cones,recession functions and properties of functions in Rockafellar and Feng Deixing's convex analysis are summarized.In the second part,by studying the recession functions of the proper convex function, we discuss the relationship between the recession direction of proper convex function and its minimal value. And we characterize the properties of the function and the existence of its minimal value. At the same time, with the help of recession direction we obtain some corresponding conclusions about the existence of this minimal value on constraint set and unconstraint set.