The New Solution Concept to Ill-Posed Bilevel Programming: Non-Antagonistic Pessimistic Solution

Xiang Li, Tiesong Hu (), Xin Wang, Ali Mahmoud and Xiang Zeng
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Xiang Li: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Tiesong Hu: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Xin Wang: Hubei Provincial Water Saving Research Center, Hubei Water Resources Research Institute, Wuhan 430070, China
Ali Mahmoud: State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China
Xiang Zeng: School of Resource and Environmental Sciences, Wuhan University, Wuhan 430079, China

Mathematics, 2023, vol. 11, issue 6, 1-13

Abstract: It is hardly realistic to assume that, under all decision circumstances, followers will always choose a solution that leads to the worst upper-level objective functional value. However, this generally accepted concept of the pessimistic solution to the ill-posed bilevel programming problems may lead to the leader’s attitude being more pessimistic vis à vis his anticipation of the follower’s decision being non-antagonistic. It will result in a wrong pessimistic solution and a greater potential of cooperation space between the leader and the followers. This paper presents a new concept of a non-antagonistic pessimistic solution with four numerical examples for bilevel programming problems from a non-antagonistic point of view. We prove that the objective function value of the non-antagonistic pessimistic solution generally dominates or is equal to the objective functional value of the pessimistic solution and the rewarding solution, and the maximum potential space for leader-follower cooperation can be overestimated in a generally applied pessimistic solution. Our research extends the concept of the pessimistic solution. It also sheds light on the insights that the non-antagonistic pessimistic solution can describe the practical potential of cooperation space between the leader and followers in non-antagonistic circumstances.

Keywords: hierarchical decision-aiding optimization scheme; ill-posed bilevel programming problem; bilevel non-antagonistic pessimistic solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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