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<p>Durea and Florea introduced the notion of cone sequential compactness of a set (J. Optim. Theory Appl. (2024) 200:1286-1308). In this paper, we give some characterizations of cone sequential compactness and establish some results by virtue of cone sequential compactness, for instance, Weierstrass-type theorem, separation theorem of convex sets and an equivalent characterization for cone upper semicontinuity of set-valued mappings. Moreover, we obtain some properties of a nonlinear scalarizing function by employing cone sequential compactness. As an application, we establish connectedness and arcwise connectedness of the solution sets for set optimization problems by utilizing cone sequential compactness.</p>

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Cone Sequential Compactness of a Set and an Application to Set Optimization Problems

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Yu Han

摘要

Durea and Florea introduced the notion of cone sequential compactness of a set (J. Optim. Theory Appl. (2024) 200:1286-1308). In this paper, we give some characterizations of cone sequential compactness and establish some results by virtue of cone sequential compactness, for instance, Weierstrass-type theorem, separation theorem of convex sets and an equivalent characterization for cone upper semicontinuity of set-valued mappings. Moreover, we obtain some properties of a nonlinear scalarizing function by employing cone sequential compactness. As an application, we establish connectedness and arcwise connectedness of the solution sets for set optimization problems by utilizing cone sequential compactness.