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Generalized polyhedral convex optimization problems

Author

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  • Nguyen Ngoc Luan

    (Hanoi National University of Education)

  • Jen-Chih Yao

    (China Medical University)

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.

Suggested Citation

  • Nguyen Ngoc Luan & Jen-Chih Yao, 2019. "Generalized polyhedral convex optimization problems," Journal of Global Optimization, Springer, vol. 75(3), pages 789-811, November.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:3:d:10.1007_s10898-019-00763-4
    DOI: 10.1007/s10898-019-00763-4
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    1. Dinh The Luc, 2016. "Multiobjective Linear Programming," Springer Books, Springer, edition 1, number 978-3-319-21091-9, July.
    2. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
    3. B. Curtis Eaves, 1971. "On Quadratic Programming," Management Science, INFORMS, vol. 17(11), pages 698-711, July.
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    Cited by:

    1. D. T. V. An & N. D. Yen, 2021. "Optimality conditions based on the Fréchet second-order subdifferential," Journal of Global Optimization, Springer, vol. 81(2), pages 351-365, October.

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