Study On ABS Algorithm For Solving A Class Of MPEC

MPEC (mathematical programs with equilibrium constraints) can be considered as a generalization of bilevel programming problem and be applied more generally than the latter. It stems from the economical problem, and has close relation with the well-known Stackelberg game. Consequently, the research of MPEC plays a very important role in many fields, such as economy, engineering design, game, decision-making and so on. However, because its feasible region is neither convex nor connected, this problem is intractable. Therefore, the nonlinear programming theory cannot be applied here directly. This problem has been solved by SQP method, implicit programming method and penalty method etc.. Nonetheless, the computation in these methods is complicated, so there exists difficulty in solving practical problem. In this paper, our goal is to find a feasible algorithm in practice.This paper discusses mainly the application of ABS algorithm into a class of MPEG. The main idea of this algorithm is as follows. Firstly, solve the non-equilibrium constrains by means of ABS algorithm, then obtain a transformation problem by taking the solution into the original problem. Secondly, solve transformation problem by using the l\ exact penalty function method and by the way of MATLAB. A proof of convergence is given, which shows that the optimal solution of the penalty function converges to that of the transformation problem. When the problem has more non-equilibrium constraints, the use of ABS algorithm will reduce constaints to a larger extent. At last, the numerical experiment is given to prove the validity of this algorithm in practical computation.