A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer-Burmeister merit function
type: Item
instance of: scholarly article
title: A nonmonotone derivative-free algorithm for nonlinear complementarity problems based on the new generalized penalized Fischer-Burmeister merit function
zbMATH Open document ID: 1279.90173
author: Jianguang Zhu
author: Hongwei Liu
author: Changhe Liu
author: Weijie Cong
published in: Numerical Algorithms
publication date: 2011-12-14T00:00:00Z
review text: The authors propose a modified Fischer-Burmeister function to solve nonlinear complementarity problems. For this purpose, they combine two approaches from \textit{J.-S. Chen} et al. [J. Comput. Appl. Math. 232, No. 2, 455--471 (2009; Zbl 1175.65070)], i.e., an additional parameter \(\lambda\in(0,1)\) is introduced and the \(p\)th root with \(p\in (1,\infty)\) is considered instead of the square root. After analyzing the properties of the new merit function, the authors state a non-monotone derivative-free algorithm for the solution of a nonlinear complementarity problem (NCP). Subsequently, global convergence of the algorithm is shown for monotone functions defining the NCP. Using stronger conditions on the nonlinear function defining the NCP the authors also prove \(r\)-linear local convergence. Finally, numerical results are presented for several MCPLIB test problems.
reviewed by: Andrea Walther
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 5988294
zbMATH Keywords: nonlinear complementarity problem
zbMATH Keywords: modified Fischer-Burmeister function
zbMATH Keywords: non-monoton derivative-free algorithm
describes a project that uses: MCPLIB
MaRDI profile type: Publication
full work available at URL: s11075-011-9471-8
OpenAlex ID: W1997829969
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DOI: 10.1007/S11075-011-9471-8
description: scientific article; zbMATH DE number 5988294