Stability of Optimal Points with Respect to Improvement Sets

Yu Han () and Ke Quan Zhao ()
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Yu Han: Jiangxi University of Finance and Economics
Ke Quan Zhao: Chongqing Normal University

Journal of Optimization Theory and Applications, 2023, vol. 199, issue 3, No 3, 904-930

Abstract: Abstract The aim of this paper is to study the stability of optimal point sets based on the improvement set E by using the scalarization method and the density results. Under the convergence of a sequence of sets in the sense of Wijsman, we derive the convergence of the sets of E-optimal points, weak E-optimal points, E-quasi-optimal points, E-Benson proper optimal points, E-super optimal points and E-strictly optimal points in the sense of Wijsman. Moreover, we obtain the semicontinuity of E-optimal point mapping, weak E-optimal point mapping, E-quasi-optimal point mapping, E-Benson proper optimal point mapping, E-super optimal point mapping and E-strictly optimal point mapping. Finally, we make a new attempt to establish Lipschitz continuity of these E-optimal point mappings under some suitable conditions.

Keywords: Vector optimization; Improvement set; Lower semicontinuity; Lipschitz continuity; 49K40; 90C29; 90C31 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02308-y

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