Convergence of solutions to set optimization problems with variable ordering structures

In this article, we consider set optimization problems with variable ordering structures. Within the framework of the set less order relation with variable ordering structures, we investigate the existence, the upper convergence, and the lower convergence of solutions to such problems in the image s...

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Bibliographic Details
Published inJournal of global optimization Vol. 91; no. 3; pp. 677 - 699
Main Authors Anh, L. Q., Hien, D. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2025
Springer Nature B.V
Subjects
Computer Science
Convergence
Mathematics
Mathematics and Statistics
Neighborhoods
Operations Research/Decision Theory
Optimization
Real Functions
Variable ordering structure
49J53
Convergence condition
Set less order relation
49K27
Set optimization problem
46N10
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Summary:In this article, we consider set optimization problems with variable ordering structures. Within the framework of the set less order relation with variable ordering structures, we investigate the existence, the upper convergence, and the lower convergence of solutions to such problems in the image spaces. For both the existence and the upper convergence of solutions, we employ new techniques to obtain various results without assuming the compactness of the constraint sets. Additionally, we utilize the domination property concerning the variable ordering cones to address the lower convergence of solutions. The obtained results are presented in several versions from different aspects for convenient comparison with existing results. Many examples are provided to illustrate the novelty of our results or to compare them with existing ones in the literature.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-024-01452-7