A Superlinearly Convergent SSLE Algorithm for Optimization Problems with Linear Complementarity Constraints

Abstract

In this paper we study a special kind of optimization problems with linear complementarity constraints. First, by a generalized complementarity function and perturbed technique, the discussed problem is transformed into a family of general nonlinear optimization problems containing parameters. And then, using a special penalty function as a merit function, we establish a sequential systems of linear equations (SSLE) algorithm. Three systems of equations solved at each iteration have the same coefficients. Under some suitable conditions, the algorithm is proved to possess not only global convergence, but also strong and superlinear convergence. At the end of the paper, some preliminary numerical experiments are reported.