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Generalized polyhedral convex optimization problems

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Abstract

Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions, weak and strong duality theorems. In particular, we show that the dual problem has the same structure as the primal problem, and the strong duality relation holds under three different sets of conditions.

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Acknowledgements

The authors would like to thank Professor Nguyen Dong Yen for valuable discussions on the subject and the three anonymous referees for valuable suggestions on this paper.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam

    Nguyen Ngoc Luan

  2. Center for General Education, China Medical University, Taichung, 40402, Taiwan

    Jen-Chih Yao

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  1. Nguyen Ngoc Luan
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  2. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

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Nguyen Ngoc Luan: This author was supported by National Foundation for Science and Technology Development (Vietnam) under grant number 101.01-2018.38 and Hanoi National University of Education under Grant Number SPHN17-02.

Jen-Chih Yao: This author was partially supported by the Grant MOST 105-2115-M-039-002-MY3.

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Luan, N.N., Yao, JC. Generalized polyhedral convex optimization problems. J Glob Optim 75, 789–811 (2019). https://doi.org/10.1007/s10898-019-00763-4

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  • DOI: https://doi.org/10.1007/s10898-019-00763-4

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