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

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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.

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Authors and Affiliations

  1. College of Mathematics and Informatics Science, Guangxi University, 530004, Nanning, P.R. China

    Jian-Ling Li & Jin-Bao Jian

  2. Department of Mathematics, Shanghai University, Baoshan, Shanghai, 200436, P.R. China

    Jian-Ling Li

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  1. Jian-Ling Li
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  2. Jin-Bao Jian
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Correspondence to Jian-Ling Li.

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Li, JL., Jian, JB. A Superlinearly Convergent SSLE Algorithm for Optimization Problems with Linear Complementarity Constraints. J Glob Optim 33, 477–510 (2005). https://doi.org/10.1007/s10898-004-2708-5

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  • DOI: https://doi.org/10.1007/s10898-004-2708-5

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