Characterizations of generalized Levitin-Polyak well-posed set optimization problems
type: Item
instance of: scholarly article
title: Characterizations of generalized Levitin-Polyak well-posed set optimization problems
zbMATH Open document ID: 1448.90099
author: S. Khoshkhabar-amiranloo
published in: Optimization Letters
publication date: 2019-03-21T00:00:00Z
review text: Set optimisation problems in normed spaces are considered. A notion of generalised Levitin-Polyak well-posedness for such problems is introduced, extending the known analogous concept of the scalar optimization setting. Generalized Levitin-Polyak well-posedness is then characterised by properties of the set of approximate solutions. Scalarizations are introduced and their well-posedness is related to that of the given problem. Further characterisations are obtained, making use of forcing functions and the Kuratowski measure of non-compactness of the approximate solutions. Sufficient conditions for well-posedness are derived.
reviewed by: Tullio Zolezzi
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 7040055
zbMATH Keywords: Levitin-Polyak well-posedness
zbMATH Keywords: set optimization
zbMATH Keywords: upper semicontinuity
zbMATH Keywords: Hausdorff convergence
zbMATH Keywords: Painlevé-Kuratowski convergence
zbMATH Keywords: cone-semicontinuity
zbMATH Keywords: cone-quasiconvexity
MaRDI profile type: Publication
full work available at URL: s11590-018-1258-6
OpenAlex ID: W2799364199
cites work: On the stability of the functional optimization problem
cites work: Q5545684
cites work: Well-posed optimization problems
cites work: Q4848726
cites work: Vector Optimization
cites work: Pointwise well-posedness in set optimization with cone proper sets
cites work: Well-posedness for set optimization problems
cites work: Generalized \(B\)-well-posedness for set optimization problems
cites work: Convexity and global well-posedness in set-optimization
cites work: Pointwise well-posedness and scalarization in set optimization
cites work: Scalarization and pointwise well-posedness for set optimization problems
cites work: Well-setness and scalarization in set optimization
cites work: Nonconvex separation theorems and some applications in vector optimization
cites work: Scalarization of Levitin–Polyak well-posed set optimization problems
cites work: Well-posedness and stability of solutions for set optimization problems
cites work: Scalar characterizations of cone-continuous set-valued maps
cites work: Q3304890
cites work: Variational Analysis
cites work: Topological structure of efficient set of optimization problem of set- valued mapping
cites work: Levitin-Polyak well-posedness for constrained quasiconvex vector optimization problems
cites work: Pointwise and global well-posedness in set optimization: a direct approach
cites work: Set-valued Optimization
cites work: Extended well-posedness of optimization problems
cites work: Q3244810
cites work: Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization
DOI: 10.1007/S11590-018-1258-6
description: scientific article; zbMATH DE number 7040055