On numerical solution of hemivariational inequalities by nonsmooth optimization methods
type: Item
instance of: scholarly article
title: On numerical solution of hemivariational inequalities by nonsmooth optimization methods
zbMATH Open document ID: 0837.49007
DOI: 10.1007/BF01100086
author: M. M. Mkel
author: M. Miettinen
author: Jaroslav Haslinger
published in: Journal of Global Optimization
publication date: 1996-05-08T00:00:00Z
review text: In the paper the authors consider numerical solution of hemivariational inequalities (HVI) by using nonsmooth, nonconvex optimization methods. First, they introduce a finite element approximation of HVI and show that it can be transformed to a problem of finding a substationary point of the corresponding potential function. Then they introduce a proximal bundle method for nonsmooth nonconvex and constrained optimization. Numerical results of a nonmonotone contact problem obtained by the developed methods are also presented.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 65M60
zbMATH DE Number: 836797
zbMATH Keywords: numerical solution
zbMATH Keywords: hemivariational inequalities
zbMATH Keywords: finite element approximation
zbMATH Keywords: proximal bundle method
Wikidata QID: Q109654988
reviewed by: P. Neittaanmäki
describes a project that uses: NSOLIB
MaRDI profile type: Publication
cites work: Shadow Prices and Duality for a Class of Optimal Control Problems
cites work: Q4162607
cites work: Optimization and nonsmooth analysis
cites work: Q3914338
cites work: Q3321366
cites work: The Cutting-Plane Method for Solving Convex Programs
cites work: Methods of descent for nondifferentiable optimization
cites work: Proximity control in bundle methods for convex nondifferentiable minimization
cites work: Approximation of optimal control problems of hemivariational inequalities
cites work: Approximation of non-monotone multivalued differential inclusions
cites work: Finite element approximation of vector-valued hemivariational problems
cites work: Q4275003
cites work: Q4004158
cites work: Q4321166
cites work: Q4323869
cites work: Hemivariational inequalities with functions fulfilling directional growth condition
cites work: Q3702572
cites work: Coercive and semicoercive hemivariational inequalities
cites work: Q4846263
cites work: A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results
full work available at URL: https://doi.org/10.1007/bf01100086
OpenAlex ID: W2064011783
Recommended article: A numerical method for a class of hemivariational inequalities
Recommended article: Q4513901
Recommended article: On the Regularization Method in Nondifferentiable Optimization Applied to Hemivariational Inequalities
Recommended article: On convergence of numerical methods for variational-hemivariational inequalities under minimal solution regularity
Recommended article: A nonsmooth Newton method for variational inequalities. II: Numerical results
Recommended article: A nonsmooth optimization approach for time-dependent hemivariational inequalities
Recommended article: Comparing nonsmooth nonconvex bundle methods in solving hemivariational inequalities
Recommended article: Numerical Analysis of Elliptic Hemivariational Inequalities
Recommended article: On the numerical solution of the problem of nonconvex optimization
Recommended article: Q3474848
description: scientific article; zbMATH DE number 836797