Existence of weakly efficient solutions in nonsmooth vector optimization
type: Item
instance of: scholarly article
title: Existence of weakly efficient solutions in nonsmooth vector optimization
zbMATH Open document ID: 1148.65044
author: Gabriel Ruiz-Garzón
author: A. Rufián-Lizana
author: L. B. Santos
author: Rojas-Medar Marko Antonio
published in: Applied Mathematics and Computation
publication date: 2008-07-11T00:00:00Z
review text: The authors consider the following two vector optimization problems 1. An infinite-dimensional problem \[ \text{Minimize }f(x)\text{ subject to }x\in K \] where \(X\) and \(Y\) are two Banach spaces, \(f: X\to Y\) is a given function and \(K\) is a nonempty subset of \(X\). 2. A finite-dimensional problem \[ \text{Minimize }f(x):=(f_1(x),\dots,f_p(x))\text{ subject to }x\in X, \] where \(f_i: \mathbb{R}^n\to\mathbb{R}\) \((i= 1,\dots, p)\) are given functions and \(X\) is a nonempty subset of \(\mathbb{R}^n\). For these problems, the existence of weakly efficient solutions are studied. The results are stated under hypotheses of generalized convexity.
reviewed by: Hans Benker
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 5300489
zbMATH Keywords: multiobjective optimization
zbMATH Keywords: nonsmooth analysis
zbMATH Keywords: invexity
zbMATH Keywords: variational-like inequalities
MaRDI profile type: Publication
full work available at URL: j.amc.2007.11.027
OpenAlex ID: W2101586881
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DOI: 10.1016/J.AMC.2007.11.027
description: scientific article; zbMATH DE number 5300489