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

Yu Han ()
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Yu Han: Jiangxi University of Finance and Economics

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 3, No 3, 25 pages

Abstract: Abstract 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.

Keywords: Cone-compactness; Nonlinear scalarizing function; Set optimization problem; Connectedness; 49J53; 54C60; 90C29 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02739-9

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