On geodesic \(E\)-convex sets, geodesic \(E\)-convex functions and \(E\)-epigraphs
type: Item
instance of: scholarly article
title: On geodesic \(E\)-convex sets, geodesic \(E\)-convex functions and \(E\)-epigraphs
zbMATH Open document ID: 1267.90172
author: Akhlad Iqbal
author: Shahid Ali
author: I. Ahmad
published in: Journal of Optimization Theory and Applications
publication date: 2013-01-29T00:00:00Z
review text: The authors generalize the concepts of \(E\)-convexity for sets, quasiconvexity for functions and the corresponding epigraphs with respect to maps \(E\) between the same Euclidean space by replacing it with a Riemannian manifold, in order to obtain the geodesic notions.
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 86A30
zbMATH DE Number: 6132203
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: geodesic \(E\)-convex set
zbMATH Keywords: \(E\)-quasiconvex function
zbMATH Keywords: \(E\)-epigraph
reviewed by: Vasile Postolică
MaRDI profile type: Publication
full work available at URL: s10957-012-0052-3
OpenAlex ID: W2014039692
cites work: Excursions into combinatorial geometry
cites work: Q5341481
cites work: Q4470339
cites work: The geometry of Minkowski spaces -- a survey. II.
cites work: On sufficiency of the Kuhn-Tucker conditions
cites work: Characterizations and applications of prequasi-invex functions.
cites work: Generalized invexity and generalized invariant monotonicity
cites work: New optimality conditions and duality results of \(G\) type in differentiable mathematical programming
cites work: Some characterizations of strongly preinvex functions
cites work: On strongly \(\alpha\)-preinvex functions
cites work: \(E\)-convex sets, \(E\)-convex functions, and \(E\)-convex programming
cites work: On the \(E\)-epigraph of an \(E\)-convex function
cites work: Nonlinear programming with \(E\)-preinvex and local \(E\)-preinvex functions
cites work: Some properties of \(E\)-convex functions
cites work: On \(E\)-convex sets, \(E\)-convex functions, and \(E\)-convex programming
cites work: Convexity along curves and indunvexity
cites work: Q4527510
cites work: Strong Geodesicα-Preinvexity and Invariantα-Monotonicity on Riemannian Manifolds
cites work: On properties of geodesic \(\eta \)-preinvex functions
DOI: 10.1007/S10957-012-0052-3
description: scientific article; zbMATH DE number 6132203