Set order relations, set optimization, and Ekeland’s variational principle
Set order relations, set optimization, and Ekeland’s variational principle
This chapter provides a brief survey on different kinds of set order relations which are used to compare the objective values of set-valued maps and play a key role to study set optimization problems. The solution concepts of set optimization problems and their relationships with respect to different kinds of set order relations are provided. The nonlinear scalarization functions for vector-valued maps as well as for set-valued maps are very useful to study the optimality solutions of vector optimization/set optimization problems. A survey of such nonlinear scalarization functions for vector-valued maps/set-valued maps is given. We give some new results on the existence of optimal solutions of set optimization problems. In the end, we gather some recent results, namely, Ekeland’s variational principle and some equivalent variational principle for set-valued maps with respect to different kinds of set order relations.
49J53, 58E30, 90C29, 90C30, 90C46
103-165
Ansari, Qamrul Hasan
66737676-6bd6-41e7-b3b1-92216dddeb0b
Sharma, Pradeep Kumar
142e7e4c-4dfa-4b91-9e7f-f2eda70380bf
Ansari, Qamrul Hasan
66737676-6bd6-41e7-b3b1-92216dddeb0b
Sharma, Pradeep Kumar
142e7e4c-4dfa-4b91-9e7f-f2eda70380bf
Ansari, Qamrul Hasan and Sharma, Pradeep Kumar
(2021)
Set order relations, set optimization, and Ekeland’s variational principle.
Laha, Vivek, Maréchal, Pierre and Mishra, S.K.
(eds.)
In Optimization, Variational Analysis and Applications - IFSOVAA-2020.
vol. 355,
Springer.
.
(doi:10.1007/978-981-16-1819-2_6).
Record type:
Conference or Workshop Item
(Paper)
Abstract
This chapter provides a brief survey on different kinds of set order relations which are used to compare the objective values of set-valued maps and play a key role to study set optimization problems. The solution concepts of set optimization problems and their relationships with respect to different kinds of set order relations are provided. The nonlinear scalarization functions for vector-valued maps as well as for set-valued maps are very useful to study the optimality solutions of vector optimization/set optimization problems. A survey of such nonlinear scalarization functions for vector-valued maps/set-valued maps is given. We give some new results on the existence of optimal solutions of set optimization problems. In the end, we gather some recent results, namely, Ekeland’s variational principle and some equivalent variational principle for set-valued maps with respect to different kinds of set order relations.
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e-pub ahead of print date: 28 July 2021
Additional Information:
Funding Information:
Acknowledgements In this research, the first author was supported by DST-SERB Project No. MTR/2017/000135 and the second author was supported by UGC-Dr. D.S. Kothari Post Doctoral Fellowship (DSKPDF) [F.4-2/2006 (BSR)/MA/19-20/0040]. All the authors acknowledge the constructive comments of the unknown referees which helped in bringing the chapter in the present form.
Venue - Dates:
Indo-French Seminar on Optimization, Variational Analysis and Applications, IFSOVAA 2020, , Varanasi, India, 2020-02-02 - 2020-02-04
Keywords:
49J53, 58E30, 90C29, 90C30, 90C46
Identifiers
Local EPrints ID: 485510
URI: http://eprints.soton.ac.uk/id/eprint/485510
ISSN: 2194-1009
PURE UUID: 1d31a2a5-c2d8-490e-9595-e5a5b62ce3e0
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Date deposited: 07 Dec 2023 17:40
Last modified: 18 Mar 2024 04:17
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Contributors
Author:
Qamrul Hasan Ansari
Author:
Pradeep Kumar Sharma
Editor:
Vivek Laha
Editor:
Pierre Maréchal
Editor:
S.K. Mishra
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