An adaptive competitive penalty method for nonsmooth constrained optimization
type: Item
instance of: scholarly article
title: An adaptive competitive penalty method for nonsmooth constrained optimization
zbMATH Open document ID: 1372.65180
author: Nezam Mahdavi-Amiri
author: M. Shaeiri
published in: Numerical Algorithms
publication date: 2017-05-15T00:00:00Z
review text: The article is a valuable contribution to nonsmooth constrained optimization. The authors develop a competitive algorithm to minimize a locally Lipschitz function constrained with locally Lipschitz constraints which is to use the \(l_I\) nonsmooth penalty function. By using second-order descent directions, the method minimizes the \(\widetilde H_k\) functions. A new adaptive approximation method for approximating Goldstein subdifferentials which lead to reduce functions and gradient evaluations significantly by using the gradient of the \(l_I\) penalty function. This article is well written, structured and explained, it contains seven sections: Section 1 on Introduction, Section 2 on Background and motivation and Section 3 on Computing descent directions, Section 4 on Boundedness of the matrices \(\widetilde H_k\) and \(\bar H_k\), Section 5 on Global convergence, Section 6 on Numerical experiments and Section 7 on Conclusion.
reviewed by: Başak Akteke-Öztürk
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6715506
zbMATH Keywords: nonsmooth optimization
zbMATH Keywords: conjugate gradient
zbMATH Keywords: constrained problem
zbMATH Keywords: global subdifferential
zbMATH Keywords: Goldstein subdifferential
zbMATH Keywords: penalty function
describes a project that uses: PNEW
describes a project that uses: LDGB
describes a project that uses: GradSamp
describes a project that uses: QSM
MaRDI profile type: Publication
full work available at URL: s11075-016-0208-6
OpenAlex ID: W2531701123
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DOI: 10.1007/S11075-016-0208-6
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description: scientific article; zbMATH DE number 6715506