Filter SQP algorithm for variational inequality problem
1.Department of Mathematics, Tongji University, Shanghai 200092, China; 2.Department of Mathematics and Physics, Shanghai Dianji University, Shanghai 201306, China; 3.Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract：The variational inequality problem was reformulated as equivalent constrained optimization problem. A new filter SQP method was proposed to solve the constrained optimization problem. Based on the difference between variational inequality problem and constrained optimization problem, a quadratic merit function was adopted at filter conditions to solve the general variational inequality problem by the filter algorithm. A trial step was obtained by SQP method combined with filter technique. Only two inequalities were needed to determine the trial step with less computation work. Under mild conditions, the global convergence was established to provide some numerical examples. The numerical results show good efficiency of the proposed method.
2012, Vol. 33 
