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A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems

Ying Zhou, Lizhi Wang
Copyright: © 2010 |Volume: 1 |Issue: 3 |Pages: 13
ISSN: 1947-9328|EISSN: 1947-9336|EISBN13: 9781609609832|DOI: 10.4018/joris.2010070101
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MLA

Zhou, Ying, and Lizhi Wang. "A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems." IJORIS vol.1, no.3 2010: pp.1-13. http://doi.org/10.4018/joris.2010070101

APA

Zhou, Y. & Wang, L. (2010). A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems. International Journal of Operations Research and Information Systems (IJORIS), 1(3), 1-13. http://doi.org/10.4018/joris.2010070101

Chicago

Zhou, Ying, and Lizhi Wang. "A New Hybrid Inexact Logarithmic-Quadratic Proximal Method for Nonlinear Complementarity Problems," International Journal of Operations Research and Information Systems (IJORIS) 1, no.3: 1-13. http://doi.org/10.4018/joris.2010070101

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Abstract

In this paper, the authors present and analyze a new hybrid inexact Logarithmic-Quadratic Proximal method for solving nonlinear complementarity problems. Each iteration of the new method consists of a prediction and a correction step. The predictor is produced using an inexact Logarithmic-Quadratic Proximal method, which is then corrected by the Proximal Point Algorithm. The new iterate is obtained by combining predictor and correction point at each iteration. In this paper, the authors prove the convergence of the new method under the mild assumptions that the function involved is continuous and monotone. Comparison to another existing method with numerical experiments on classical NCP instances demonstrates its superiority.

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