Smoothing methods for nonsmooth, nonconvex minimization
type: Item
instance of: scholarly article
title: Smoothing methods for nonsmooth, nonconvex minimization
zbMATH Open document ID: 1266.90145
author: Michael Martin Xiaojun Chen
published in: Mathematical Programming. Series A. Series B
publication date: 2012-11-02T00:00:00Z
review text: The author considers the optimization problem \[ f(x)\to\min,\quad\text{subject to }x\in X, \] where \(X\) is a closed convex subset of \(\mathbb{R}^n\) and \(f:\mathbb{R}^n\to \mathbb{R}\) is continuous and almost everywhere differentiable in \(X\). Special attention is devoted to the case of a nonsmooth and nonconvex objective function, which is not in general locally Lipschitzian. For solving such optimization problems, smoothing methods are proposed using smoothing functions. Properties of the smoothing functions and conditions ensuring the convergence of the proposed methods to a stationary point of the original problem are presented. The last section of the paper is devoted to the numerical implementation of the proposed procedures.
reviewed by: Karel Zimmermann
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49M37
Mathematics Subject Classification ID: 65K10
zbMATH DE Number: 6101845
zbMATH Keywords: nonconvex minimization
zbMATH Keywords: nonsmooth minimization
zbMATH Keywords: smoothing methods
zbMATH Keywords: stochastic variational inequality problems
describes a project that uses: GradSamp
describes a project that uses: ElemStatLearn
MaRDI profile type: Publication
full work available at URL: s10107-012-0569-0
OpenAlex ID: W2098000549
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Smoothing methods for nonsmooth, nonconvex minimization (DOI)
DOI: 10.1007/S10107-012-0569-0