Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation

Lam Quoc Anh (), Tran Quoc Duy (), Dinh Vinh Hien (), Daishi Kuroiwa () and Narin Petrot ()
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Lam Quoc Anh: Cantho University
Tran Quoc Duy: Ton Duc Thang University
Dinh Vinh Hien: University of Science, Vietnam National University Ho Chi Minh City
Daishi Kuroiwa: Shimane University
Narin Petrot: Naresuan University

Journal of Optimization Theory and Applications, 2020, vol. 185, issue 2, No 6, 416-432

Abstract: Abstract This article investigates stability conditions for set optimization problems with the set less order relation in the senses of Panilevé–Kuratowski and Hausdorff convergence. Properties of various kinds of convergences for elements in the image space are discussed. Taking such properties into account, formulations of internal and external stability of the solutions are studied in the image space in terms of the convergence of a solution sets sequence of perturbed set optimization problems to a solution set of the given problem.

Keywords: Set optimization; Set less order relation; Internal stability; External stability; 49M37; 90C30; 65K05; 47J20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-020-01657-2

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