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Predictor-corrector method for nonlinear complementarity problem

Predictor-corrector method for nonlinear complementarity problem Recently, Ye et al. proved that the predictor-corrector method proposed by Mizuno et al. maintains $$O\left( {\sqrt n L} \right)$$ -iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a $$(\sqrt n \log ({1 \mathord{\left/ {\vphantom {1 \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }))$$ -iteration complexity while maintaining the quadratic asymptotic convergence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Predictor-corrector method for nonlinear complementarity problem

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02025887
Publisher site
See Article on Publisher Site

Abstract

Recently, Ye et al. proved that the predictor-corrector method proposed by Mizuno et al. maintains $$O\left( {\sqrt n L} \right)$$ -iteration complexity while exhibiting the quadratic convergence of the dual gap to zero under very mild conditions. This impressive result becomes the best-known in the interior point methods. In this paper, we modify the predictor-corrector method and then extend it to solving the nonlinear complementarity problem. We prove that the new method has a $$(\sqrt n \log ({1 \mathord{\left/ {\vphantom {1 \varepsilon }} \right. \kern-\nulldelimiterspace} \varepsilon }))$$ -iteration complexity while maintaining the quadratic asymptotic convergence.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 17, 2005

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