On strong pseudoconvexity in nonlinear programming duality
type: Item
instance of: scholarly article
title: On strong pseudoconvexity in nonlinear programming duality
zbMATH Open document ID: 0713.90058
author: T. Weir
published in: Opsearch
publication date: 1990-01-01T00:00:00Z
review text: Let S be an open convex set in \(R^ n\) and let f: \(S\to R\) be differentiable. If there exists an arbitrary positive functional p: \(S\times S\to R\) satisfying f(y)-f(x)\(\geq p(x,y)(y-x)^ T\nabla f(x,y)\) for all x,y\(\in S\), then f is said to be strongly pseudoconvex with respect to p(x,y) over s. Clearly, strong pseudoconvexity is a weaker condition than convexity but stronger than pseudoconvexity. The author proves duality theorems for a pair of dual programs first introduced by \textit{B. Mond} and himself [in: Generalized concavity in optimization and economics, Proc. NATO Adv. Study Inst., Vancouver/Can. 1980, 263-279 (1981; Zbl 0538.90081)] under the strong pseudoconvexity assumption on the constraint function.
Mathematics Subject Classification ID: 90C26
Mathematics Subject Classification ID: 49N15
Mathematics Subject Classification ID: 90C32
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4174669
zbMATH Keywords: strong pseudoconvexity
zbMATH Keywords: duality theorems
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4174669