Journal of Optimization Theory and Applications

, Volume 142, Issue 2, pp 323–342 | Cite as

Optimality Conditions for Vector Optimization Problems

Article

Abstract

In this paper, some necessary and sufficient optimality conditions for the weakly efficient solutions of vector optimization problems (VOP) with finite equality and inequality constraints are shown by using two kinds of constraints qualifications in terms of the MP subdifferential due to Ye. A partial calmness and a penalized problem for the (VOP) are introduced and then the equivalence between the weakly efficient solution of the (VOP) and the local minimum solution of its penalized problem is proved under the assumption of partial calmness.

Keywords

Vector optimization problem Optimality condition Partial calmness Exact penalization MP subdifferential 

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China
  2. 2.School of Mathematics and InformationChina West Normal UniversityNanchongPeople’s Republic of China
  3. 3.Institute of Applied MathematicsNational Cheng-Kung UniversityTainanTaiwan
  4. 4.National Center for Theoretical SciencesTainanTaiwan

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