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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| Published in | Journal of global optimization Vol. 91; no. 3; pp. 677 - 699 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.03.2025
Springer Nature B.V |
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| Online Access | Get full text |
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| Abstract | 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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| AbstractList | 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. |
| Author | Anh, L. Q. Hien, D. V. |
| Author_xml | – sequence: 1 givenname: L. Q. surname: Anh fullname: Anh, L. Q. organization: Department of Mathematics, Teacher College, Cantho University – sequence: 2 givenname: D. V. orcidid: 0000-0002-0790-6281 surname: Hien fullname: Hien, D. V. email: hiendv@huit.edu.vn organization: Department of Mathematics, Ho Chi Minh City University of Industry and Trade |
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| Keywords | Variable ordering structure 49J53 Convergence condition Set less order relation 49K27 Set optimization problem 46N10 |
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| Title | Convergence of solutions to set optimization problems with variable ordering structures |
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