Appl Math Optim 54:17–46 (2006) © 2006 Springer Science+Business Media, Inc. A Strongly and Superlinearly Convergent SQP Algorithm for Optimization Problems with Linear Complementarity Constraints∗

Abstract. This paper discusses a kind of optimization problem with linear com-plementarity constraints, and presents a sequential quadratic programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modi-fication of the SQP algorithm proposed by Fukushima et al. [Computational Op-timization and Applications, 10 (1998), 5–34], and is based on a reformulation of complementarity condition as a system of linear equations. At each iteration, one quadratic programming and one system of equations needs to be solved, and a curve search is used to yield the step size. Under some appropriate assumptions, including the lower-level strict complementarity, but without the upper-level strict comple-mentarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence. Some preliminary numerical results are reported