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H. Bonnel and J. Morgan, “Semivectorial Bilevel Optimization Problem: Penalty Approach,” Journal of Optimization Theory and Applications, Vol. 131, No. 3, 2006, pp. 365-382. doi:10.1007/s10957-006-9150-4

has been cited by the following article:

• TITLE: Generating Efficient Solutions in Bilevel Multi-Objective Programming Problems

  AUTHORS: Calice Olivier Pieume, Patrice Marcotte, Laure Pauline Fotso, Patrick Siarry

  KEYWORDS: Multi-Objective Programming; Bilevel Programming; Efficient Solution; Efficient Edge; Hierarchical Systems

  JOURNAL NAME: American Journal of Operations Research, Vol.3 No.2, March 29, 2013

  ABSTRACT: In this paper, we address bilevel multi-objective programming problems (BMPP) in which the decision maker at each level has multiple objective functions conflicting with each other. Given a BMPP, we show how to construct two artificial multiobjective programming problems such that any point that is efficient for both the two problems is an efficient solution of the BMPP. Some necessary and sufficient conditions for which the obtained result is applicable are provided. A complete procedure of the implementation of an algorithm for generating efficient solutions for the linear case of BMPP is presented. A numerical example is provided to illustrate how the algorithm operates.