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A regularized projection method for complementarity problems with non-Lipschitzian functions
Author(s):
Goetz
Alefeld;
Xiaojun
Chen.
Journal:
Math. Comp.
77
(2008),
379-395.
MSC (2000):
Primary 90C33, 65G20
Posted:
June 20, 2007
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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.
References:
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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:
10.1090/S0025-5718-07-02025-X
PII:
S 0025-5718(07)02025-X
Keywords:
Complementarity problems,
non-Lipschitzian continuity,
regularization,
projection,
error bounds.
Received by editor(s):
June 8, 2006
Posted:
June 20, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
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