Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization
type: Item
instance of: scholarly article
title: Six set scalarizations based on the oriented distance: continuity, convexity and application to convex set optimization
author: B. Jiménez
author: V. Novo
author: A. Vílchez
author: L. Huerga
published in: Mathematical Methods of Operations Research
publication date: 2021-07-14T00:00:00Z
Mathematics Subject Classification ID: 06A75
Mathematics Subject Classification ID: 49J53
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 7371318
zbMATH Keywords: oriented distance
zbMATH Keywords: set optimization
zbMATH Keywords: set order relations
zbMATH Keywords: scalarization in set optimization
zbMATH Keywords: convexity
zbMATH Keywords: continuity
zbMATH Keywords: Lagrange multipliers
MaRDI profile type: Publication
full work available at URL: s00186-020-00736-4
OpenAlex ID: W3122781822
cites work: Characterizations of set relations with respect to variable domination structures via oriented distance function
cites work: Q5142516
cites work: Four types of nonlinear scalarizations and some applications in set optimization
cites work: Q3782303
cites work: A unified characterization of nonlinear scalarizing functionals in optimization
cites work: Characterizations of set order relations and constrained set optimization problems via oriented distance function
cites work: First-order optimality conditions in set-valued optimization
cites work: Lagrange multipliers for \(\varepsilon \)-Pareto solutions in vector optimization with nonsolid cones in Banach spaces
cites work: Nonconvex separation theorems and some applications in vector optimization
cites work: Variational methods in partially ordered spaces
cites work: Scalarization in set optimization with solid and nonsolid ordering cones
cites work: Lagrange multipliers for set-valued optimization problems associated with coderivatives
cites work: A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization
cites work: Duality for Set-Valued Measures of Risk
cites work: Nonlinear scalarizing functions in set optimization problems
cites work: Continuity and convexity of a nonlinear scalarizing function in set optimization problems with applications
cites work: Some useful set-valued maps in set optimization
cites work: Nonconvex scalarization in set optimization with set-valued maps
cites work: Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces
cites work: New order relations in set optimization
cites work: A set scalarization function based on the oriented distance and relations with other set scalarizations
cites work: Characterization of set relations through extensions of the oriented distance
cites work: Six set scalarizations based on the oriented distance: properties and application to set optimization
cites work: Q4992445
cites work: Set-valued Optimization
cites work: Q3220809
cites work: Q4252562
cites work: Continuity of cone-convex functions
cites work: Q3066883
cites work: Relationships between the oriented distance functional and a nonlinear separation functional
cites work: Q4235027
cites work: Analysis II. Convex analysis and approximation theory. Transl. from the Russian by D. Newton
cites work: A new nonlinear scalarization function and applications
cites work: Degrees of Efficiency and Degrees of Minimality
DOI: 10.1007/S00186-020-00736-4
description: scientific article; zbMATH DE number 7371318