| Nonsmooth optimization is an important branch in nonlinear programming,technology development and application in nowadays,we often encounter the phenomenon of non smooth.Semismooth functions as an important class of nonsmooth functions of nonsmooth optimization,because of its good smooth information is be concerned by many scholars in recent years,and has been made in a lot of progress,and it has been applied in many practical problems.In this paper,the application of UV-decomposition theory to study a special class of semi-smooth functions--composite semi-smooth functions unconstrained optimization problems,the specific form is as follows:where,Y?·?=?f1,f 2,…,fm?T:Rn?Rm is vector valued function,f i:Rn?R,i=1,2,…,m is semi-smooth functions,E:Rm?R is local Lipschitz functions.The UV-decomposition theory was first introdused by C.Lemaréchal,F.Oustry,and so on.Mainly used the smooth information of functions to study the convex function's two order approximation,and then get a new effective method for solving convex optimization problems.Considering the complexity of this paper functions structure,direct application of the UV-decomposition theory is certain difficulty,therefore this paper mainly through the smooth information to semi-smooth functions,combining the UV-decomposition theory,to solve this kind of semi-smooth unconstrained optimization problems.This paper will discuss the following three aspects.Firstly,we introduce the definition of semi-smooth functions and some of its basic properties.Secondly,we study the basic properties of a class of complex semi-smooth functions.Finally,give the definition of this kind of composite semi-smooth function's U-Lagrange functions,and its optimal solution sets W?u?,discuss the basic properties of this kind of composite semi-smooth function's U-Lagrange functions,researched the UV-decomposition algorithm of the composite semi-smooth functions of unconstrained optimization problems and proved the algorithm convergence. |
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