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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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