Research About Constraints Condition Of Mathematical Programs With Stochastic Equilibrium Constraints

Stochastic programming and complementarity problems, as important parts of mathematical programming, have been widely applied in many fields such as engineering design, optimal control, information technology and economic equilibrium. At present. the hot research of this kind of problem is the constraint conditions of extreme-value problem which combining stochastic programming and menta-mentarity problems.This paper mainly focuses on basic theory to stochastic equilibrium constrained optimization problems. The key point is properties of constraint conditions, so we do much work on the state of the properties of constraint conditions in the paper. Here, we deform the constraint conditions in three different views, and discuss the existence of solutions for the problems. The first method is expected residual regeneration method. which connect the constraints into equality constraints. Then we study the continuous differentiability and gradient semismoothness of the equation, because it is an important evaluation criterion for the convergence of SQP algorithm. The second method to be used is penalty weighted approximation method, which get new extremum problems through the deformation of original problem. Then we discuss the existence and convergence of solutions through consider the penalty function constructed, and give algorithm in the end. The third method is similar with the second method, but the differences are that we construct new extremum problems from different angles, however the content discussed is consistent.Firstly. we introduce the research significance of stochastic equilibrium constrained optimization problems and their research status; in the second chapter we give some prepare knowledge. and introduce some properties of the constraint conditions of stochastic equilibrium constrained optimization problems; in the third chapter we discuss the constraint conditions in three parts, namely, we deform the constraint conditions with three different methods, and solve the problems according to the specific form respectively; in the fourth chapter the numerical experiments are proposed. In the final chapter of this paper, we make a summary and propose ideas for the next stage of the study.