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Approximate weak efficiency of the set-valued optimization problem with variable ordering structures

Author

Listed:
  • Zhiang Zhou

    (Chongqing University of Technology)

  • Wenbin Wei

    (Chongqing Normal University)

  • Fei Huang

    (Chongqing University of Technology)

  • Kequan Zhao

    (Chongqing Normal University)

Abstract

In locally convex spaces, we introduce the new notion of approximate weakly efficient solution of the set-valued optimization problem with variable ordering structures (in short, SVOPVOS) and compare it with other kinds of solutions. Under the assumption of near $$\mathcal {D}(\cdot )$$ D ( · ) -subconvexlikeness, we establish linear scalarization theorems of (SVOPVOS) in the sense of approximate weak efficiency. Finally, without any convexity, we obtain a nonlinear scalarization theorem of (SVOPVOS). We also present some examples to illustrate our results.

Suggested Citation

  • Zhiang Zhou & Wenbin Wei & Fei Huang & Kequan Zhao, 2024. "Approximate weak efficiency of the set-valued optimization problem with variable ordering structures," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-13, October.
    • Handle: RePEc:spr:jcomop:v:48:y:2024:i:3:d:10.1007_s10878-024-01211-0
    DOI: 10.1007/s10878-024-01211-0
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    References listed on IDEAS

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    1. Shokouh Shahbeyk & Majid Soleimani-damaneh & Refail Kasimbeyli, 2018. "Hartley properly and super nondominated solutions in vector optimization with a variable ordering structure," Journal of Global Optimization, Springer, vol. 71(2), pages 383-405, June.
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