Convergence of convex-concave saddle functions: Applications to convex programming and mechanics
type: Item
instance of: scholarly article
title: Convergence of convex-concave saddle functions: Applications to convex programming and mechanics
zbMATH Open document ID: 0667.49009
DOI: 10.1016/S0294-1449(16)30335-3
author: D. Azé
author: Hédy Attouch
author: Roger J.-B. Wets
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78164
review text: In the framework of the epi-convergence theory the authors generalize to reflexive Banach spaces some results on the bicontinuity with respect to the epitopology of the Legendre-Fenchel transform on the space of proper, lower semicontinuous, convex functions defined on \(R^ n.\) It is shown that the appropriate notion of convergence for saddle function is that of epi/hypo-convergence. The results are applied to study the stability of the optimal solutions and associated multipliers of convex programs. Applications in mechanics are also considered. The first one concerns homogenization of elasticity, where primal and dual variable are respectively equal to displacement vector fields and stress tensor fields. The homogenization process is studied by introduction of the associated Lagrangians, with their epi/hypo- convergence that provides the convergence of their saddle points. The second one deals with the convergence of the primal/dual solutions in a reinforcement problem when the thickness of the reinforced zone goes to zero.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 74E05
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90C55
Mathematics Subject Classification ID: 54A20
zbMATH DE Number: 4092201
zbMATH Keywords: epi-convergence
zbMATH Keywords: bicontinuity
zbMATH Keywords: stability
zbMATH Keywords: multipliers of convex programs
zbMATH Keywords: elasticity
reviewed by: Marco Codegone
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4092201