A new smoothing Broyden-like method for solving the mixed complementarity problem with a \(P_{0}\)-function
type: Item
instance of: scholarly article
title: A new smoothing Broyden-like method for solving the mixed complementarity problem with a \(P_{0}\)-function
zbMATH Open document ID: 1208.90172
author: Jia Tang
author: Sanyang Liu
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-07-20T00:00:00Z
review text: In this paper, the authors propose a new smoothing Broyden-like algorithm for solving the mixed complementarity problem (MCP) based on a new perturbed mid function. The algorithm considered here combines the advantages of quasi-Newton method of local superlinear convergence and a floating genetic algorithm in group search, and global convergence. In addition, existence and continuity of a smooth path for solving the mixed complementarity problem with a \(P_0\)-function are discussed in this paper. The authors also show that, under suitable conditions, the iterates generated by the proposed method converge globally to a solution of the mixed complementarity problem. Finally, making use of smooth and semismooth techniques, the authors prove the local superlinear convergence of the proposed algorithm under mild assumptions. Some numerical results are reported to show that the new method is feasible and effective.
reviewed by: Samir Kumar Neogy
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 90C53
Mathematics Subject Classification ID: 90C59
zbMATH DE Number: 5757783
zbMATH Keywords: mixed complementarity problem
zbMATH Keywords: smoothing function
zbMATH Keywords: genetic algorithm
zbMATH Keywords: quasi-Newton method
zbMATH Keywords: smoothing Broyden-like algorithm
zbMATH Keywords: global convergence
zbMATH Keywords: superlinear convergence
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2009.10.002
OpenAlex ID: W2025971692
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DOI: 10.1016/J.NONRWA.2009.10.002
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description: scientific article; zbMATH DE number 5757783