A Truly Globally Convergent Feasible Newton-Type Method for Mixed Complementarity Problems
De Ren Han 11 School of Mathematics and Computer Science, Nanjing Normal University Nanjing 210097, China
Typical solution methods for solving mixed complementarity problems either generate feasible iterates but have to solve relatively complicated subproblems such as quadratic programs or linear complementarity problems, or (those methods) have relatively simple subproblems such as system of linear equations but possibly generate infeasible iterates. In this paper, we propose a new Newton-type method for solving monotone mixed com- plementarity problems, which ensures to generate feasible iterates, and only has to solve a system of well-conditioned linear equations with reduced dimension per iteration. Without any regularity assumption, we prove that the whole sequence of iterates converges to a so- lution of the problem (truly globally convergent). Furthermore, under suitable conditions, the local superlinear rate of convergence is also established.
Key words: Mixed complementarity problems; Newton-type methods; Global convergence; Superlinear convergence.