Second order duality for nondifferentiable multiobjective programming problem involving \((F, \alpha , \rho , d)-V\)-type I functions
type: Item
instance of: scholarly article
title: Second order duality for nondifferentiable multiobjective programming problem involving \((F, \alpha , \rho , d)-V\)-type I functions
zbMATH Open document ID: 1194.90083
author: B. E. Eshmatov
published in: Optimization Letters
publication date: 2010-05-03T00:00:00Z
review text: The authors define classes of second-order (semi-strictly) \((F, \alpha,\rho,d)\)-V-type I and second-order (strictly) pseudoquasi \((F,\tilde \alpha,\tilde \rho,d)\)-V-type I functions. They study the multiobjective program \[ \min (f_i(x)+ (x^TB_ix)^{\frac{1}{2}}, i=1, \ldots, k) \] subject to \(x \in X =\{x: g(x) \leqq 0\}\), where \(f_i(x)\) are twice differentiable on \(X\) and \(B_i\) are \(n\times n\) positive semidefinite matrices. For both Mangasarian type and Mond-Weir type duals of this problem they prove weak, strong, and strict converse duality results.
reviewed by: Matthias Ehrgott
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 90C46
zbMATH DE Number: 5703324
zbMATH Keywords: multiobjective optimization
zbMATH Keywords: generalized convexity
zbMATH Keywords: second order duality
MaRDI profile type: Publication
full work available at URL: s11590-009-0159-0
OpenAlex ID: W1966299923
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DOI: 10.1007/S11590-009-0159-0
description: scientific article; zbMATH DE number 5703324