Improving the robustness of descent-based methods for semismooth equations using proximal perturbations |
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Authors: | Stephen C Billups |
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Institution: | (1) University of Colorado at Denver, Department of Mathematics, Campus Box 170, P.O. Box 173364, Denver, CO 80217-3364, USA, e-mail: sbillups@carbon.cudenver.edu, US |
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Abstract: | A common difficulty encountered by descent-based equation solvers is convergence to a local (but not global) minimum of an
underlying merit function. Such difficulties can be avoided by using a proximal perturbation strategy, which allows the iterates
to escape the local minimum in a controlled fashion. This paper presents the proximal perturbation strategy for a general
class of methods for solving semismooth equations and proves subsequential convergence to a solution based upon a pseudomonotonicity
assumption. Based on this approach, two sample algorithms for solving mixed complementarity problems are presented. The first
uses an extremely simple (but not very robust) basic algorithm enhanced by the proximal perturbation strategy. The second
uses a more sophisticated basic algorithm based on the Fischer-Burmeister function. Test results on the MCPLIB and GAMSLIB
complementarity problem libraries demonstrate the improvement in robustness realized by employing the proximal perturbation
strategy.
Received July 15, 1998 / Revised version received June 28, 1999?Published online November 9, 1999 |
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Keywords: | : proximal perturbations – pseudomonotonicity – semismooth equations – complementarity problems |
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