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Optimality Conditions for Vector Optimization Problems

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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.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, People’s Republic of China

    N. J. Huang

  2. School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, People’s Republic of China

    J. Li

  3. Institute of Applied Mathematics, National Cheng-Kung University, Tainan, 700, Taiwan

    S. Y. Wu

  4. National Center for Theoretical Sciences, Tainan, Taiwan

    S. Y. Wu

Authors
  1. N. J. Huang
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  2. J. Li
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  3. S. Y. Wu
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Corresponding author

Correspondence to N. J. Huang.

Additional information

Communicated by P.M. Pardalos.

This work was supported by the National Natural Science Foundation of China (10671135), the Specialized Research Fund for the Doctoral Program of Higher Education (20060610005) and the National Natural Science Foundation of Sichuan Province (07ZA123).

The authors thank Professor P.M. Pardalos and the referees for comments and suggestions.

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Huang, N.J., Li, J. & Wu, S.Y. Optimality Conditions for Vector Optimization Problems. J Optim Theory Appl 142, 323–342 (2009). https://doi.org/10.1007/s10957-009-9514-7

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