Merit function and global algorithm for box constrained variational inequalities

摘要

The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desi- able properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original prob- lem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.