Levitin-Polyak well-posedness for vector optimization problems in linear spaces. (2nd January 2023)

• Record Type: Journal Article
• Authors: Quoc Anh, Lam; Huu Danh, Nguyen; Ngoc Tam, Tran
• Is Part Of: Optimization. Volume 72:Number 1(2023)
• Page Start: 9
• Page End: 35
• Publication Date: 2023-01-02
• Subjects: Vector optimization problems -- well-posedness -- existence conditions -- generalized semicontinuity -- Zorn's Lemma; 49J27 -- 49K40 -- 90C31; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2142470
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we deal with vector optimization problems where the images of the objective maps are given in linear spaces not endowed with any topological structure. Firstly, we propose new concepts of semicontinuity of vector-valued maps acting from metric spaces into linear ones and discuss their properties and characterizations. Next, using Zorn's Lemma and these properties, we formulate existence conditions for such problems. Then, we introduce two notions of Levitin-Polyak well-posedness for the reference problems, and study sufficient conditions for their fulfillment, as well as relationships of these notions. Finally, using the Kuratowski measure of noncompactness, several metric characterizations of such well-posedness properties for vector optimization problems are investigated. Many examples are given to analyze our results.