Scalarization and Well-Posedness for Set Optimization Problems Involving General Set Less Relations

Yue Zeng (), Zai-Yun Peng (), Christane Tammer (), Jen-Chih Yao () and Ke Deng ()
Additional contact information
Yue Zeng: Sichuan University
Zai-Yun Peng: Yunnan Normal University
Christane Tammer: Martin-Luther-University Halle-Wittenberg
Jen-Chih Yao: China Medical University
Ke Deng: Sichuan University

Journal of Optimization Theory and Applications, 2025, vol. 207, issue 2, No 18, 23 pages

Abstract: Abstract The aim of this paper is to investigate the scalarization and well-posedness for set optimization problems where the solution concept is given by the lower set less relation induced by general sets. First, we propose three kinds of well-posedness for set optimization problems via general sets and study their relationships. Moreover, some sufficient conditions for these kinds of well-posedness for set optimization problems via free-disposal set are obtained under the Hausdorff P-continuity of the objective mapping of the set optimization problem, rather than the continuity in the sense of Berge. By employing a nonlinear scalarization technique by means of the oriented distance function, corresponding scalar optimization problems are established, and the relationship between solutions of the set optimization problem where the solution concept is given by the lower set less relation induced by co-radiant sets and solutions of the corresponding scalarized problem is also discussed. Furthermore, we also give some characterization of well-posedness for set optimization problem through two scalar optimization problems. Some examples are given to illustrate the main results.

Keywords: Set optimization; Well-posedness; General domination sets; Nonlinear scalarization function; 49J53; 49K40; 90C48 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02784-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:207:y:2025:i:2:d:10.1007_s10957-025-02784-4

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-025-02784-4

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().