Stability of efficient solutions to set optimization problems
type: Item
instance of: scholarly article
title: Stability of efficient solutions to set optimization problems
zbMATH Open document ID: 1475.49028
author: L. Q. Anh
author: T. Q. Duy
author: Dinh Vinh Hien
published in: Journal of Global Optimization
publication date: 2021-04-28T00:00:00Z
review text: The authors consider set optimization problems in real topological Hausdorff spaces as well as the Painleve-Kuratowski convergence of Pareto minimal elements. In particular, they study stability properties of solution sets of corresponding perturbed set optimization problems. Finally, they introduce a compact convergence concept in order to study the internal stability of solution sets.
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 7340610
zbMATH Keywords: set optimization problem
zbMATH Keywords: Pareto minimal solution
zbMATH Keywords: internal and external stability
zbMATH Keywords: compact convergence
zbMATH Keywords: domination property
reviewed by: Jan-Joachim Rückmann
MaRDI profile type: Publication
full work available at URL: s10898-020-00932-w
OpenAlex ID: W3044146131
cites work: Tykhonov well-posedness for lexicographic equilibrium problems
cites work: Convergence of solutions to set optimization problems with the set less order relation
cites work: Stability for Parametric Vector Quasi-Equilibrium Problems With Variable Cones
cites work: Gap functions and Hausdorff continuity of solution mappings to parametric strong vector quasiequilibrium problems
cites work: Set-valued optimization in welfare economics
cites work: A note on lower semicontinuity of minimal points
cites work: Continuity of minimal points with applications to parametric multiple objective optimization
cites work: Q4277838
cites work: Weak minimal elements and weak minimal solutions of a nonconvex set-valued optimization problem
cites work: Stability of minimizers of set optimization problems
cites work: Scalarization in set optimization with solid and nonsolid ordering cones
cites work: Convergence of solutions of a set optimization problem in the image space
cites work: Set optimization and applications -- the state of the art. From set relations to set-valued risk measures
cites work: Well-posedness and stability of solutions for set optimization problems
cites work: Differentiability Properties of a Parametric Consumer Problem
cites work: Sensitivity analysis of a stationary point set map under total perturbations. I: Lipschitzian stability
cites work: Sensitivity analysis of a stationary point set map under total perturbations. II: Robinson stability
cites work: Vector Optimization
cites work: New order relations in set optimization
cites work: External and internal stability in set optimization
cites work: Stability of minimal solutions to parametric set optimization problems
cites work: A unified minimal solution in set optimization
cites work: Q4703393
cites work: Convergence of Minimal Sets in Convex Vector Optimization
cites work: Variational Analysis and Applications
cites work: Q3700345
cites work: Differentiability of Relations and Differential Stability of Perturbed Optimization Problems
cites work: A systematization of convexity and quasiconvexity concepts for set-valued maps, defined byl-type andu-type preorder relations
cites work: On set containment characterizations for sets described by set-valued maps with applications
cites work: Sequential characterizations of approximate solutions in convex vector optimization problems with set-valued maps
cites work: Stability and sensitivity analysis in multiobjective nonlinear programming
cites work: Directionally generalized differentiation for multifunctions and applications to set-valued programming problems
cites work: Convergence of the relative Pareto efficient sets
cites work: Continuity of the solution set mappings to a parametric set optimization problem
DOI: 10.1007/S10898-020-00932-W
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description: scientific article; zbMATH DE number 7340610