Invex generalizations of some duality results
type: Item
instance of: scholarly article
title: Invex generalizations of some duality results
zbMATH Open document ID: 0657.90091
published in: Opsearch
publication date: 1988-01-01T00:00:00Z
review text: Consider the pair of symmetric dual problems: \[ (P)\quad f(x,y)\quad \to \quad \min,\quad (x,y)\quad \in \quad P, \] \[ (D)\quad g(x,y)\quad \to \quad \max,\quad (x,y)\quad \in \quad D, \] \[ P=\{(x,y)\in C_ 1\times C_ 2:\quad K_ y'(x,y)\in C^*_ 2\},\quad D=\{(x,y)\in C_ 1\times C_ 2:\quad K_ x'(x,y)\in C^*_ 1\}, \] where \(C_ 1\), \(C_ 2\) are closed convex cones and K: \({\mathcal U}(C_ 1\times C_ s)\to R\) is a differentiable function. Under some generalized convexity conditions, the invexity of f and g, a weak duality theorem is proved. A similar theorem is stated for a pair of nonlinear mixed integer programming problems.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 4074835
zbMATH Keywords: nonconvex duality
zbMATH Keywords: symmetric dual problems
zbMATH Keywords: closed convex cones
zbMATH Keywords: generalized convexity conditions
zbMATH Keywords: invexity
zbMATH Keywords: weak duality theorem
zbMATH Keywords: nonlinear mixed integer programming
author: Sudarsan Nanda
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4074835