Epsilon efficiency
type: Item
instance of: scholarly article
title: Epsilon efficiency
zbMATH Open document ID: 0573.90085
DOI: 10.1007/BF00940762
published in: Journal of Optimization Theory and Applications
publication date: 1986-01-01T00:00:00Z
review text: This paper considers the extension of \(\epsilon\)-optimality for scalar problems to vector maximization problems, or efficiency problems, which have m objective functions defined on a set \(X\subseteq {\mathbb{R}}^ n\). It is shown that the natural extension of the scalar \(\epsilon\)-optimality concepts (viz, given \(\epsilon >0\), given a solution set S, if \(x\in S\) there exists an efficient solution y with \(\| f(x)-f(y)\| \leq \epsilon\), and given an efficient solution y, there exists an \(x\in S\) with \(\| f(x)-f(y)\| \leq \epsilon)\) do not hold for some methods used. Six concepts of \(\epsilon\)-efficient sets are introduced and examined, to a very limited extent, in the context of five methods used for generating efficient points or near efficient points. In doing so, a distinction is drawn between methods in which the surrogate optimizations are carried out exactly, and those where terminal \(\epsilon\)-optimal solutions are obtained.
Mathematics Subject Classification ID: 90C31
Mathematics Subject Classification ID: 90B50
Mathematics Subject Classification ID: 90C40
zbMATH DE Number: 3916037
zbMATH Keywords: efficient solution
zbMATH Keywords: efficient sets
zbMATH Keywords: weighting factors
zbMATH Keywords: constrained objectives
zbMATH Keywords: penalty functions
zbMATH Keywords: ideal points
zbMATH Keywords: Markov decision processes
zbMATH Keywords: epsilon-optimality
zbMATH Keywords: vector optimization
author: D. J. White
MaRDI profile type: Publication
cites work: Characterizations of efficient sets by constrained objectives
cites work: Q3309761
cites work: Multi-objective infinite-horizon discounted Markov decision processes
cites work: Duality theory in multiobjective programming
cites work: Q5514145
cites work: Q4120209
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full work available at URL: https://doi.org/10.1007/bf00940762
OpenAlex ID: W2914548405
description: scientific article; zbMATH DE number 3916037