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Mathematics of Computation

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A regularized projection method for complementarity problems with non-Lipschitzian functions


Authors: Goetz Alefeld and Xiaojun Chen
Journal: Math. Comp. 77 (2008), 379-395
MSC (2000): Primary 90C33, 65G20
DOI: https://doi.org/10.1090/S0025-5718-07-02025-X
Published electronically: June 20, 2007
MathSciNet review: 2353958
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Abstract: We consider complementarity problems involving functions which are not Lipschitz continuous at the origin. Such problems arise from the numerical solution for differential equations with non-Lipschitzian continuity, e.g. reaction and diffusion problems. We propose a regularized projection method to find an approximate solution with an estimation of the error for the non-Lipschitzian complementarity problems. We prove that the projection method globally and linearly converges to a solution of a regularized problem with any regularization parameter. Moreover, we give error bounds for a computed solution of the non-Lipschitzian problem. Numerical examples are presented to demonstrate the efficiency of the method and error bounds.


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Additional Information

Goetz Alefeld
Affiliation: Institute of Applied and Numerical Mathematics, University of Karlsruhe (Karlsruhe Institute of Technology KIT), D-76128 Karlsruhe, Germany
Email: goetz.alefeld@math.uni-karlsruhe.de

Xiaojun Chen
Affiliation: Department of Mathematical Sciences, Hirosaki University, 036-8561 Hirosaki, Japan
Email: chen@cc.hirosaki-u.ac.jp

DOI: https://doi.org/10.1090/S0025-5718-07-02025-X
Keywords: Complementarity problems, non-Lipschitzian continuity, regularization, projection, error bounds.
Received by editor(s): June 8, 2006
Published electronically: June 20, 2007
Article copyright: © Copyright 2007 American Mathematical Society