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

Authors: 

Lam Quoc Anh, Tran Quoc Duy*, Dinh Vinh Hien, Daishi Kuroiwa, Narin Petrot

Source title: 
Journal of Optimization Theory and Applications, 185: 416-432, 2020 (ISI)
Academic year of acceptance: 
2020-2021
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.