Order-preserving transformations and applications
type: Item
instance of: scholarly article
title: Order-preserving transformations and applications
zbMATH Open document ID: 1036.90059
DOI: 10.1023/A:1025495204834
author: Dinh The Luc
author: Alberto Cambini
author: Laura Martein
published in: Journal of Optimization Theory and Applications
publication date: 2004-02-12T00:00:00Z
review text: The paper considers properties of efficient sets of vector optimization (or multi-objective optimization) problems. Linear transformations of ordering cones (for ordering efficient solutions) are considered with special emphasis on studying their effects on the order relations. Sufficient conditions for preserving a given order are derived as well as some calculus rules for subdifferentials of convex vector-valued functions. The paper is concluded by some optimality conditions for weak efficiency.
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 2041229
zbMATH Keywords: partial orders
zbMATH Keywords: efficient points
zbMATH Keywords: generalized convex functions
zbMATH Keywords: subdifferentials
reviewed by: Kaisa Miettinen
MaRDI profile type: Publication
cites work: Q3701188
cites work: Q5555984
cites work: Proper efficiency with respect to cones
cites work: On the notion of proper efficiency in vector optimization
cites work: Proper solutions of vector optimization problems
cites work: On the properly efficient points of nonconvex sets
cites work: Theory of multiobjective optimization
cites work: Subdifferentiability of Convex Functions with Values in an Ordered Vector Space.
cites work: On three concepts of quasiconvexity in vector optimization
cites work: Q4296846
cites work: Q4257356
cites work: Some new classes of generalized concave vector-valued functions
cites work: Convex vector functions and their subdifferential
cites work: Subdifferential characterization of quasiconvex and convex vector functions
cites work: Generalized Quasiconvex Mappings and Vector Optimization
cites work: Optimization and nonsmooth analysis
cites work: A Multiplier Rule for Multiobjective Programming Problems with Continuous Data
full work available at URL: a:1025495204834
OpenAlex ID: W1554741491
description: scientific article; zbMATH DE number 2041229