Set-valued increasing-along-rays maps and well-posed set-valued star-shaped optimization
type: Item
instance of: scholarly article
title: Set-valued increasing-along-rays maps and well-posed set-valued star-shaped optimization
zbMATH Open document ID: 1114.49026
author: Rong Hu
author: Ya Ping Fang
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-04-26T00:00:00Z
review text: The authors introduce a class of set-valued increasing-along-rays maps and present some properties of set-valued increasing-along-rays maps. It is shown that the increasing-along-rays property of a set-valued map is close related to the corresponding set-valued star-shaped optimization. By means of increasing-along-rays property, the stability and well-posedness of set-valued star-shaped optimization is investigated.
Mathematics Subject Classification ID: 49K40
Mathematics Subject Classification ID: 49J53
zbMATH DE Number: 5146745
zbMATH Keywords: set valued maps
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.09.073
OpenAlex ID: W2076976522
cites work: Q3786295
cites work: Q4298951
cites work: Vector equilibrium problems with generalized monotone bifunctions
cites work: Minty variational inequalities, increase-along-rays property and optimization
cites work: Existence of solutions and star-shapedness in Minty variational inequalities
cites work: On variational principles, level sets, well-posedness, and \(\epsilon\)-solutions in vector optimization
cites work: Well-posed optimization problems
cites work: Increasing-along-rays property, vector optimization and well-posedness
cites work: Variational methods in partially ordered spaces
cites work: Extended well-posedness properties of vector optimization problems
cites work: Pointwise well-posedness of perturbed vector optimization problems in a vector-valued variational principle
cites work: Q4871548
cites work: Well-posedness and convexity in vector optimization
cites work: Well-posedness and scalarization in vector optimization
cites work: Convergence of Minimal Sets in Convex Vector Optimization
cites work: Abstract convexity:examples and applications
cites work: Minimizing increasing star-shaped functions based on abstract convexity
cites work: Seperability of Star-Shaped Sets and its Application to an Optimization Problem
cites work: Set convergences: A survey and a classification
cites work: Generalized semicontinuity and existence theorems for cone saddle points
cites work: On the stability of the functional optimization problem
cites work: Is every radiant function the sum of quasiconvex functions?
cites work: Well-posedness criteria in optimization with application to the calculus of variations
cites work: Extended well-posedness of optimization problems
DOI: 10.1016/J.JMAA.2006.09.073
description: scientific article; zbMATH DE number 5146745