A class of semilocal \(E\)-preinvex functions and its applications in nonlinear programming
type: Item
instance of: scholarly article
title: A class of semilocal \(E\)-preinvex functions and its applications in nonlinear programming
zbMATH Open document ID: 1235.90152
DOI: 10.1155/2012/629194
author: Hehua Jiao
author: Xinying Pai
author: Sanyang Liu
published in: Journal of Applied Mathematics
publication date: 2012-04-04T00:00:00Z
review text: Summary: A kind of generalized convex set, called as local star-shaped \(E\)-invex set with respect to \(\eta\), is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal \(E\)-preinvex functions, which is a generalization of semi-\(E\)-preinvex functions and semilocal \(E\)-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6021721
Wikidata QID: Q58906277
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/629194
OpenAlex ID: W1983690603
cites work: Q3932576
cites work: Q3328295
cites work: Sufficient Conditions for Global Minima of Suitably Convex Functionals from Variational and Control Theory
cites work: Generalizations of convex and related functions
cites work: Sufficient optimality conditions using generalized convex functions
cites work: Optimality and duality in nonlinear programming involving semilocally preinvex and related functions
cites work: Q4347197
cites work: Optimality and Duality in Fractional Programming Involving Semilocally Convex and Related Functions
cites work: Optimality and duality in fractional multiple objective programming involving semilocally preinvex and related functions.
cites work: \(E\)-convex sets, \(E\)-convex functions, and \(E\)-convex programming
cites work: Some properties of semi-\(E\)-convex functions.
cites work: Semilocal E-convexity and semilocal E-convex programming
cites work: Q3405094
cites work: Nonlinear programming with \(E\)-preinvex and local \(E\)-preinvex functions
cites work: Some properties of semi-\(E\)-preinvex maps in Banach spaces
cites work: Multiple objective fractional programming involving semilocally type I-preinvex and related functions
cites work: Q3890448
cites work: Perfect duality for convexlike programs
DBLP publication ID: journals/jam/JiaoLX12
description: scientific article; zbMATH DE number 6021721