Sufficient optimality criteria and duality for multiobjective variational problems with \(V\)-invexity
type: Item
instance of: scholarly article
title: Sufficient optimality criteria and duality for multiobjective variational problems with \(V\)-invexity
zbMATH Open document ID: 0820.90096
author: R. N. Mukherjee
author: S. K. Mishra
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1995-09-14T00:00:00Z
review text: Recently, Jeyakumar and Mond introduced the concept of \(V\)-invexity. A vector of differentiable functions is said to be \(V\)-invex if each component function is invex with respect to some strictly positive multiple of \(\eta\). Here the concept of \(V\)-invexity (as well as \(V\)- pseudo-invexity and \(V\)-quasi-invexity) is defined for a vector of continuous functions \(f(t, x,\dot x)\). These concepts are then applied to obtain sufficiency and duality results for the continuous nonlinear multiobjective programming problem \[ V\text{-}\min\Biggl(\int^ T_ 0 f_ 1(t, x,\dot x) dt,\;\int^ T_ 0 f_ 2(t, x, \dot x)dt,\dots, \int^ T_ 0 f_ k(t, x, \dot x)dt\Biggr) \] subject to \(x(0)= \alpha\), \(x(T)= \beta\), \(g(t, x,\dot x)\leq 0\), \(0\leq t\leq T\), where \(V\)-min means find a weak minimum.
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 49N15
zbMATH DE Number: 695827
zbMATH Keywords: \(V\)-invexity
zbMATH Keywords: sufficiency and duality results
zbMATH Keywords: continuous nonlinear multiobjective programming
reviewed by: Bertram Mond
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 695827