Quasidifferentiability in nonsmooth, nonconvex mechanics
type: Item
instance of: scholarly article
title: Quasidifferentiability in nonsmooth, nonconvex mechanics
zbMATH Open document ID: 0869.73079
DOI: 10.1007/BF01100082
author: V. F. Demyanov
author: Georgios E. Stavroulakis
author: Lyudmila N. Polyakova
published in: Journal of Global Optimization
publication date: 1997-09-11T00:00:00Z
review text: The modern structural analysis and engineering applications require the study of structures with material laws which involve complete ascending or descending vertical branches with monotone and generally nonmonotone graphs. Adhesive contact mechanics, softening and locking effects in concrete and geomaterials, tension cracking effects in masonry structures belong to category of problems where methods of nonsmooth structural analysis are used. The general scheme used in structural analysis and computational mechanics consists of defining a potential energy function and producing the governing equations and inequalities as well as optimality conditions for this potential function, taking into account equality or inequality constraints. The aim of this paper is to review the development of solution methods for such problems. The methods considered employ nonsmooth nonconvex mechanics and quasidifferentiable and codifferentiable optimization of problems involving variational inequalities. Remark. The concept of quasidifferential was given by \textit{V. F. Dem'yanov}, \textit{L. N. Polyakova} and \textit{A. M. Rubinov} in the work [On one generalization of the concept of subdifferential, All Union Conf. on Dynamic Control, 79-84, Sverdlovsk (1979)].
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74P10
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 90C90
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 49J52
zbMATH DE Number: 836793
zbMATH Keywords: potential energy function
zbMATH Keywords: optimality conditions
zbMATH Keywords: quasidifferentiable and codifferentiable optimization
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01100082
OpenAlex ID: W2024492108
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description: scientific article; zbMATH DE number 836793