Miscellaneous incidences of convergence theories in optimization and nonlinear analysis. I: Behavior of solutions
type: Item
instance of: scholarly article
title: Miscellaneous incidences of convergence theories in optimization and nonlinear analysis. I: Behavior of solutions
zbMATH Open document ID: 0856.49012
DOI: 10.1007/BF01027105
author: Jean-Paul Penot
published in: Set-Valued Analysis
publication date: 1994-10-13T00:00:00Z
review text: The author investigates the dependence of the solution set for the inclusion \(y \in F(x)\) in a normed space \(X\) on perturbations of \(y\) and \(F\). For a functional \(f : X \to \overline R\), the behavior of the correspondence \(f \mapsto m_f : = \inf \{f(x) : x \in X\}\) and the multimaps \(f \mapsto S_f : = \{x \in X : f(x) = m_f\}\), \(f \mapsto S_f (\varepsilon) : = \{x \in X : f(x) \leq m_f + \varepsilon\}\) is studied.
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 627475
zbMATH Keywords: minimization
zbMATH Keywords: sensitivity
zbMATH Keywords: set-valued maps
zbMATH Keywords: solution set
zbMATH Keywords: inclusion
zbMATH Keywords: multimaps
reviewed by: Valerii V. Obukhovskij
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01027105
OpenAlex ID: W2006102520
description: scientific article; zbMATH DE number 627475