Qualitative properties of solutions to set optimization problems

In this paper, we consider set optimization problems involving set relations. Using the well-known KKM-Fan Lemma and relaxed convexity assumptions, we study existence conditions for these problems. Moreover, we introduce parametric nonlinear scalarization functions for sets and study their propertie...

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Bibliographic Details
Published in:Computational & applied mathematics 2021-03, Vol.40 (2), Article 66
Main Authors: Anh, Lam Quoc, Danh, Nguyen Huu, Duoc, Pham Thanh, Tam, Tran Ngoc
Format: Article
Language:English
Subjects:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Continuity (mathematics)
Convexity
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Optimization
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Summary:In this paper, we consider set optimization problems involving set relations. Using the well-known KKM-Fan Lemma and relaxed convexity assumptions, we study existence conditions for these problems. Moreover, we introduce parametric nonlinear scalarization functions for sets and study their properties. By utilizing the concerning functions, we investigate relationships between set optimization problems and equilibrium problems. Finally, sufficient conditions for the Hölder continuity of solution maps to such problems via equilibrium problems are established.
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01458-x