Solving linear fractional bilevel programs.
The authors give a geometrical characterization of the optimal solution to the linear fractional bilevel programming (LFBP) problem in terms of what is called a boundary feasible extreme point. It is assumed that the second level optimal solution sets are singletons. The results extend the characterization proved by \textit{Y. H. Liu} and \textit{S. M. Hart} [Eur. J. Oper. Res. 73, 164--166 (1994; Zbl 0806.90084)] for the linear bilevel programming problem. Based on this property the authors show that the \(K\)th-best algorithm can be used to solve the LFBP problem. This algorithm was first proposed by \textit{W. F. Bialas} and \textit{M. H. Karwan} [Manage. Sci. 30, 1004--1020 (1984; Zbl 0559.90053)] for solving the linear bilevel programming problem. An example is included to illustrate the application of the algorithm. Finally, the last section includes some remarks on quasiconcave bilevel problems for which the characterization of the optimal solution is still valid and the \(K\)th-best algorithm can be applied to solve them.
scientific article; zbMATH DE number 2021244