A Strongly and Superlinearly Convergent SQP Algorithm for Optimization Problems with Linear Complementarity Constraints |
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Authors: | Jin-Bao Jian Jian-Ling Li Xing-De Mo |
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Institution: | (1) College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, People's Republic of China;(2) Department of Mathematics, Shanghai University, Shanghai 200444, People's Republic of China |
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Abstract: | This paper discusses a kind of optimization problem with linear complementarity constraints, and presents a sequential quadratic
programming (SQP) algorithm for solving a stationary point of the problem. The algorithm is a modification of the SQP algorithm
proposed by Fukushima et al. Computational Optimization 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
complementarity for the inequality constraints, the algorithm is proved to possess strong convergence and superlinear convergence.
Some preliminary numerical results are reported. |
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Keywords: | |
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