Some topological properties of solution sets in partially ordered set optimization
Some topological properties of solution sets in partially ordered set optimization
In this paper, we study some topological properties, in particular, arcwise connectedness and connectedness of solution sets in set optimization, where the acting space is equipped with partial set order relations. We obtain continuity, generalized convexity, and natural quasi arcwise connectedness of the nonlinear scalarization function and use them to study some topological properties and convergence of efficient and weak efficient solution sets in partially ordered set optimization. We also employ derived results to vector-valued game theory with uncertainty.
Arcwise connectedness, Game theory, Generalized convexity, Nonlinear scalarization, Set optimization
163-180
Sharma, Pradeep Kumar
142e7e4c-4dfa-4b91-9e7f-f2eda70380bf
Khushboo,
1e0599bc-cebe-451b-8c78-9d5eb843c24b
Sharma, Pradeep Kumar
142e7e4c-4dfa-4b91-9e7f-f2eda70380bf
Khushboo,
1e0599bc-cebe-451b-8c78-9d5eb843c24b
Sharma, Pradeep Kumar and Khushboo,
(2023)
Some topological properties of solution sets in partially ordered set optimization.
Journal of Applied and Numerical Optimization, 5 (1), .
(doi:10.23952/jano.5.2023.1.11).
Abstract
In this paper, we study some topological properties, in particular, arcwise connectedness and connectedness of solution sets in set optimization, where the acting space is equipped with partial set order relations. We obtain continuity, generalized convexity, and natural quasi arcwise connectedness of the nonlinear scalarization function and use them to study some topological properties and convergence of efficient and weak efficient solution sets in partially ordered set optimization. We also employ derived results to vector-valued game theory with uncertainty.
More information
e-pub ahead of print date: 1 April 2023
Additional Information:
Funding Information:
The authors are grateful to the handling editor and the anonymous referee for their valuable comments and suggestions, which helped to improve the previous draft of the paper. The first author was supported by UGC-Dr. D.S. Kothari Post Doctoral Fellowship No. F.4-2/2006 (BSR)/MA/19-20/0040.
Keywords:
Arcwise connectedness, Game theory, Generalized convexity, Nonlinear scalarization, Set optimization
Identifiers
Local EPrints ID: 485506
URI: http://eprints.soton.ac.uk/id/eprint/485506
ISSN: 2562-5527
PURE UUID: e45d4f87-a631-4ef8-9107-fcca21d48194
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Date deposited: 07 Dec 2023 17:39
Last modified: 18 Mar 2024 04:17
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Contributors
Author:
Pradeep Kumar Sharma
Author:
Khushboo
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