Some Research On A Class Of Mathematical Program With Equilibrium Constraints

In this paper, we study a class of Mathematical Program with Equilibrium Constraints, which is referred to as MPEC?1?: minf?x? s.t.g_i?x?< 0,i= 1,…,m h_i?x?= 0,i= l,…,p 0?x₁ ? x₂?0 With the rapid development of computer technology in recent years, solving the mathematical program with equilibrium constraints problems emerge in endlessly. The most commonly using are Sequential Quadratic Programming method ?for short SQP method?, penalty method and complementary relaxation method. A DC algorithm is a new method. This article is established on the basis of the theoretical framework, which is set up by the author Matthieu M. and Rafael C. This paper tentatively applies this approach in solving MPEC?1? problems, and obtains some achievements. In that follows, we will introduce the main job, which may be summarized as follows:1. In chapter 2, because general constraint qualification is not set up in any MPEC?1?' feasible points. Therefore we discussed the suitable constraint qualification of the problem M-PEC?1?, shorthand for MPEC-LICQ. According to sufficient conditions based on the DC problem of local minimizer and local minimizer, which is strongly stationary point, of the mathematical program with equilibrium constraints problem in the corresponding MPEC Linear Indepen-dence Constraint Qualification ?MPEC Linear Independence Constraint Qualification, referred MPEC-LICQ? condition. We study the problem MPEC?1?, then give four sufficient conditions for a class of mathematical program with equilibrium constraints problems'strongly stationary points.2. In chapter 3, according to the DC Algorithm ?DC Algorithm, referred DCA?, which is put forward by the author Matthieu M. and Rafael C. The algorithm is improved and perfected, such that the algorithm iteration of sequence limit point can have better properties. Then combined with the actual situation of the problem MPEC?1?, we present the specific algorithm of the problem MPEC?1?, put forward and proved that the algorithm is convergent to the strong and stable condition in the corresponding constraint qualification.