On the numerical treatment of nonconvex energy problems of mechanics
type: Item
instance of: scholarly article
title: On the numerical treatment of nonconvex energy problems of mechanics
zbMATH Open document ID: 0864.73079
DOI: 10.1007/BF01100087
author: E. K. Koltsakis
author: E. S. Mistakidis
author: M. A. Tzaferopoulos
published in: Journal of Global Optimization
publication date: 1996-01-23T00:00:00Z
review text: The paper presents three numerical methods for the treatment of nonconvex nonsmooth minimization problems arising in structural and continuum mechanics. All the methods approximate the nonconvex energy problem by convex subproblems. The first method is based on the decomposition of the contingent cone of the superpotential of the problem into convex components. The second one uses an iterative scheme in order to approximate the hemivariational inequality problem by a sequence of variational inequalities. Finally, the third method is based on the fact that nonconvexity in mechanics is closely related to irreversible effects that affects the Hessian matrix of the superpotential. All methods are applied to solve the same problems, and the obtained results are compared.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 836798
zbMATH Keywords: convex minimization
zbMATH Keywords: decomposition of contingent cone
zbMATH Keywords: nonsmooth minimization problems
zbMATH Keywords: convex subproblems
zbMATH Keywords: superpotential
zbMATH Keywords: iterative scheme
zbMATH Keywords: hemivariational inequality
zbMATH Keywords: sequence of variational inequalities
zbMATH Keywords: irreversible effects
zbMATH Keywords: Hessian matrix
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 836798