A Smooth Approximation Method For Stochastic Complementarity Problems With Chance Constraint

Stochastic nonlinear complementarity problem is a hot topic in the field of stochastic programming,and has been widely used in real life,such as economy,information,engineering and other fields.Due to the uncertainty of the parameters involved,the stochastic nonlinear complementarity problem model with chance constraints has attracted much attention.The Chance Constraint Optimization Model has attracted many scholars at home and abroad since it was proposed.In view of the non-convex and non-smooth property of this kind of model,many effective numerical algorithms have appeared in the literature,such as the convex approximation method,D.C.approximation method,smooth approximation method,etc.In this paper,a smooth approximation method for stochastic nonlinear complementarity problems with chance constraints is discussed based on CHKS smoothing sum function.Specific research results are as follows:In chapter 1,introduces the research status of stochastic complementarity problem and chance constrained optimization problem,as well as the relevant preliminary knowledge.In chapter 2,the smooth approximation function of characteristic function is constructed based on CHKS smooth sum function,and the properties of the approximate function are discussed.In chapter 3,we discuss the equivalence problem of stochastic nonlinear complementarity problem with chance constraint.Firstly,Fischer-Burmeister(F-B)function and its properties are introduced.Secondly,based on the F-B function,the constraint conditions of the nonlinear stochastic complementarity problem were reconstructed into stochastic equations,and the corresponding chance constrained optimization problem was constructed.Finally,based on the CHKS smoothing sum function,the smoothing approximation function of the chance constraint function is constructed,and the corresponding smoothing approximation problem is established,and the convergence is analyzed.In chapter 4,the sample mean approximation method for solving smooth approximation problem is studied.Firstly,the sample average approximation function of the smooth approximation function is constructed,and the corresponding sample mean approximation problem is established,which is transformed into an unconstrained minimization problem.Combined with the concrete example,the random generator is used to generate the independent identical distribution samples,and the Matlab program is used to solve the problem The results show that the solution of the approximate sample mean problem is the approximate solution of the stochastic nonlinear complementarity problem.