The SC~1 Property Of Expected Residual Functions Arising From Stochastic Complementarity Problems

Stochastic programming and complementarity problems,as important parts of math-ematical programming,have wide applications in many fields such as engineering de-sign, optimal control,information technology and economic equilibrium.The expected residual minimization(ERM) is one of effective ways to solve the stochastic comple-mentarity problems(SCP).This thesis is mainly concerned with the SC~1 property of the expected residual function arising from the stochastic complementarity problems.The ERJVI formulation aims at minimizing an expected residual defined by an NCP function,and we define the objective function as ERM-NCP function.The SC~1 property is a crucial condi-tion for superlinear convergence of the SQP method for solving nonlinear program-ming problems that are once,but not twice,continuously differentiable.By choosing different NCP functions,the objective function presents different properties and the ERM formulation generally provides different solutions.Throughout the thesis,we employ two NCP functions called the "min" function and the generalized Fischer-Burmeister (FB)function.We first make a short review of SCP and presents some of the fundamental concepts and conclusions which are the main tools for our theoretical analysis.In chapter 2,we prove the SC~1 property of the expected residual function arising from SCP when the generalized FB NCP function is employed.In chapter 3,we obtain the semismooth property of the expected residual function arising from SCP when the "min" NCP function is adopted,and we also show the SC~1 property of it at the strictly feasible points of SCP.In the last chapter,we conclude the thesis and give a plan for the next stage.