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<p>In this paper, we employ Kasimbeyli’s conic scalarization function and relax certain conditions from the existing literature to provide an equivalent scalar representation of set order relations in normed spaces. Furthermore, we apply these results to derive optimality conditions for set-valued optimization problems. By introducing suitable sets and a convex cone in the image space, we establish optimality conditions for various concepts of robust solutions for uncertain multiobjective optimization problems. Several examples are given to illustrate the accuracy and usefulness of the results.</p>

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Characterization of set order relations and set optimization problems via conic scalarization

  • 期刊论文

  • 发表日期：

    2025年10月14日

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  • Madhusudan Das,
  • Debdas Ghosh,
  • Jen-Chih Yao,
  • Xiaopeng Zhao

摘要

In this paper, we employ Kasimbeyli’s conic scalarization function and relax certain conditions from the existing literature to provide an equivalent scalar representation of set order relations in normed spaces. Furthermore, we apply these results to derive optimality conditions for set-valued optimization problems. By introducing suitable sets and a convex cone in the image space, we establish optimality conditions for various concepts of robust solutions for uncertain multiobjective optimization problems. Several examples are given to illustrate the accuracy and usefulness of the results.