Pieume, C.O., Marcotte, P., Fotso, L.P. and Siarry, P. (2013) Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems. American Journal of Operations Research, 3, 289-298.
https://doi.org/10.4236/ajor.2013.32026

has been cited by the following article:

• TITLE: Solving Quasiconcave Bilevel Programming Problem

  AUTHORS: Dahande Balme, Laure Pauline Fotso

  KEYWORDS: Bilevel Multiobjective Programming Problem, Quasiconcave Bilevel Programming Problem, Efficient Set

  JOURNAL NAME: American Journal of Operations Research, Vol.7 No.2, March 31, 2017

  ABSTRACT: In this paper, we find the solution of a quasiconcave bilevel programming problem (QCBPP). After formulating a Bilevel Multiobjective Programming Problem (BMPP), we characterize its leader objective function and its feasible set. We show some necessary and sufficient conditions to establish a convex union of set of efficient point, an efficient set at the QCBPP. Based on this result, we formulate and solve a new QCBPP. Finally, we illustrate our approach with a numerical example.