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Isolated and Proper Efficiencies in Semi-Infinite Vector Optimization Problems

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Abstract

This paper deals with a nonsmooth semi-infinite multiobjective/vector optimization problem (SIMOP, for short). We first establish necessary and sufficient conditions for (local) strongly isolated solutions and (local) positively properly efficient solutions of an SIMOP. Then, we propose a dual problem to the SIMOP under consideration and examine weak and strong duality relations between them.

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Acknowledgements

This research was partially supported by the Grant NSC 102-2221-E-037-004-MY3.

This work was supported by a grant from the NAFOSTED (Vietnam) and the Grant NSC 99-2221-E-037-007-MY3.

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Authors and Affiliations

  1. Department of Mathematics & Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

  2. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

  3. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Jen-Chih Yao

Authors
  1. Thai Doan Chuong
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  2. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

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Chuong, T.D., Yao, JC. Isolated and Proper Efficiencies in Semi-Infinite Vector Optimization Problems. J Optim Theory Appl 162, 447–462 (2014). https://doi.org/10.1007/s10957-013-0425-2

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  • DOI: https://doi.org/10.1007/s10957-013-0425-2

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