Enhanced efficiency in multi-objective optimization
type: Item
instance of: scholarly article
title: Enhanced efficiency in multi-objective optimization
zbMATH Open document ID: 1322.90086
published in: Journal of Optimization Theory and Applications
publication date: 2014-11-03T00:00:00Z
review text: The authors introduce and study a generalized notion of proper efficiency in multi-objective optimization, denoted as \(\alpha\)-proper efficiency. After giving some preliminaries and definitions in Section 2, the main results are presented in Section 3. In particular, two characterizations of \(\alpha\)-proper efficiency are given: one in terms of the existence of an exact penalty function (Theorem 3.1), and one in terms of the stability of the associated parametric problem (Theorem 3.2). Moreover, a set of verifiable conditions for an efficient solution to be \(\alpha\)-properly efficient in polynomial multi-objective optimization is given (Theorem 3.3). Finally, some examples are presented to illustrate the results obtained. In Section 4, an example is given to demonstrate that \(\alpha\)-proper efficiency may not hold for problems with \(C^{\infty}\)-functions as objective functions.
reviewed by: Frank Werner
Mathematics Subject Classification ID: 90C29
zbMATH DE Number: 6363592
zbMATH Keywords: efficient solution
zbMATH Keywords: \(\alpha\)-properly efficient solution
zbMATH Keywords: polynomial multi-objective optimization
zbMATH Keywords: exact penalization
MaRDI profile type: Publication
full work available at URL: s10957-013-0486-2
OpenAlex ID: W1984772859
cites work: Proper efficiency and the theory of vector maximization
cites work: Vector optimization. Set-valued and variational analysis.
cites work: Variational Analysis
cites work: On efficient solutions in vector optimization
cites work: Optimization on metric and normed spaces
cites work: Global error bounds for convex quadratic inequality systems*
cites work: Perturbation analysis of a condition number for convex inequality systems and global error bounds for analytic systems
cites work: On characterizations of proper efficiency for nonconvex multiobjective optimization
cites work: The Vector Maximization Problem: Proper Efficiency and Stability
cites work: Optimization and nonsmooth analysis
DOI: 10.1007/S10957-013-0486-2
author: Y. Jiang
author: S. Deng
description: scientific article; zbMATH DE number 6363592