A Modified Active Set Algorithm For Mathematical Programs With Linear Complementarity Constraints

We consider a mathematical program with linear complementary constraints (MPLCC). It is a kind of special nonlinear program because of its complementary constraints. We will propose a modified active set algorithm for MPLCC. At every iteration, in order to eliminate the complementary constraints, we design a relaxed problem with linear constraints. Rosen projective gradient method is used to find the approximated KKT points of relaxed problem, and then the index set is updated until the minimal solution is obtained. We prove the feasibility and convergence of the modified active set algorithm and get conclusion that under the uniform linear independence constraint qualification (LICQ) , every cluster point of the sequence generated by the algorithm is a B stationary point of MPLCC. In the end, we give some numerical experience of the modified algorithm and get the useful results.There are five chapters in the thesis. First, we introduce the problem briefly; second, we introduce traditional active set algorithm for mathematical program with complementary constraint and the Rosen projective gradient method for the mathematical program linear constraints, and then discuss the property and convergence of the algorithm. The main part of this paper is in the third and fourth chapters. In former chapter we analyze the modified active set algorithm and prove the convergence in next chapter. In the fifth chapter we carry out the numerical results of the modified algorithm. The sixth chapter summarizes the main result of this paper.