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Generalized Polyhedral DC Optimization Problems

Author

Listed:
  • Vu Thi Huong

    (Vietnam Academy of Science and Technology)

  • Duong Thi Kim Huyen

    (Phenikaa University)

  • Nguyen Dong Yen

    (Vietnam Academy of Science and Technology)

Abstract

The problem of minimizing the difference of two lower semicontinuous, proper, convex functions (a DC function) on a nonempty closed convex set in a locally convex Hausdorff topological vector space is studied in this paper. The focus is made on the situations where either the second component of the objective function is a generalized polyhedral convex function or the first component of the objective function is a generalized polyhedral convex function and the constraint set is generalized polyhedral convex. Various results on optimality conditions, the local solution set, the global solution set, and solution algorithms via duality are obtained. Useful illustrative examples are considered.

Suggested Citation

  • Vu Thi Huong & Duong Thi Kim Huyen & Nguyen Dong Yen, 2025. "Generalized Polyhedral DC Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 207(1), pages 1-28, October.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:1:d:10.1007_s10957-025-02769-3
    DOI: 10.1007/s10957-025-02769-3
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    References listed on IDEAS

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    1. Nguyen Thi Hang & Nguyen Dong Yen, 2016. "On the Problem of Minimizing a Difference of Polyhedral Convex Functions Under Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 617-642, November.
    2. Nguyen Ngoc Luan & Jen-Chih Yao, 2019. "Generalized polyhedral convex optimization problems," Journal of Global Optimization, Springer, vol. 75(3), pages 789-811, November.
    3. Nguyen Ngoc Luan & Nguyen Dong Yen, 2024. "Strong Duality and Solution Existence Under Minimal Assumptions in Conic Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 203(2), pages 1083-1102, November.
    4. Hoai An Le Thi & Tao Pham Dinh, 2024. "Open issues and recent advances in DC programming and DCA," Journal of Global Optimization, Springer, vol. 88(3), pages 533-590, March.
    5. X. Q. Yang & N. D. Yen, 2010. "Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 113-124, October.
    Full references (including those not matched with items on IDEAS)

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