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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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