Lagrangemultiplier rules for approximate solutions in vector optimization

Caiping Liu; Heungwing Lee

doi:10.3934/jimo.2012.8.749

Article Contents

2012, Volume 8, Issue 3: 749-764. Doi: 10.3934/jimo.2012.8.749

This issue Previous Article A sequential convex program method to DC program with joint chance constraints Next Article Identification for systems governed by nonlinear interval differential equations

Lagrange multiplier rules for approximate solutions in vector optimization

Caiping Liu^1, and
Heungwing Lee^2,

1.
College of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Received: December 31, 2011

Revised: February 29, 2012

Published: June 2012

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Abstract

In Asplund space, Lagrange multiplier rules for approximate solutions of nonsmooth vector optimization problems are studied. The relationships between the vector and the scalar optimization problems are established. And the optimality conditions of approximate solutions for vector optimization are obtained. Moreover, the vector variational inequalities are considered by applying the partial results given in this paper.

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Mathematics Subject Classification: Primary: 90C29, 49J52, 90C46.

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