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Mathematical Programs with Vector Optimization Constraints

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Abstract

In this paper, we introduce mathematical programs with vector optimization constraints. For these problems, we establish two models in both the weak Pareto solution and Pareto solution setting. Some new existence results are obtained under rather weak conditions. We establish also equivalences between mathematical programs with vector optimization constraints and mathematical programs with vector variational inequality constraints.

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Authors and Affiliations

  1. Assistant Professor, Department of Information Management, Cheng Shiu University, Niaosong, Kaohsiung, Taiwan, ROC

    Y. C. Liou

  2. Professor, Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong

    X. Q. Yang

  3. Professor, Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC

    J. C. Yao

Authors
  1. Y. C. Liou
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  2. X. Q. Yang
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  3. J. C. Yao
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Additional information

This research was partially supported by a grant from the National Science Council of the ROC. The authors thank the referees for helpful suggestions and comments.

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Liou, Y.C., Yang, X.Q. & Yao, J.C. Mathematical Programs with Vector Optimization Constraints. J Optim Theory Appl 126, 345–355 (2005). https://doi.org/10.1007/s10957-005-4720-4

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  • DOI: https://doi.org/10.1007/s10957-005-4720-4

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