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Bilevel Quadratic Fractional/Quadratic Problem

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Modelling, Computation and Optimization in Information Systems and Management Sciences

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 359))

Abstract

The bilevel programming problems are useful tools for solving the hierarchy decision problems. The purpose of this paper is to find the optimality conditions and a solution procedure to solve a bilevel quadratic fractional-quadratic programming problem in which the leader’s objective is quadratic fractional and the follower’s objective is quadratic. The variables associated with both the level problems are related by linear constraints. The proposed method is based on Karush-Kuhn-Tucker conditions and a related bilevel linear fractional-quadratic problem is constructed in which the leader’s objective is linear fractional and the follower’s objective is quadratic in order to obtain an optimal solution of a bilevel quadratic fractional-quadratic programming problem. The main idea behind our method is to scan the basic feasible solutions of the related bilevel linear fractional- quadratic programming problem in a systematic manner till an optimal solution of the problem is obtained.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, USTHB, BP 32, El-Alia, 16111, Algiers, Algeria

    Nacéra Maachou

  2. LaROMaD Laboratory, USTHB University, BP 32, El-Alia, 16111, Algiers, Algeria

    Mustapha Moulaï

Authors
  1. Nacéra Maachou
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  2. Mustapha Moulaï
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Corresponding author

Correspondence to Nacéra Maachou .

Editor information

Editors and Affiliations

  1. Laboratory of Theoretical and Applied Computer Science, University of Lorraine-Metz, Metz, France

    Hoai An Le Thi

  2. Laboratory of Mathematics, National Institute for Applied Sciences-Rouen, Rouen, France

    Tao Pham Dinh

  3. Division of Knowledge Management Systems Institute of Informatics (I-32), Wroclaw University of Technology, Wroclaw, Poland

    Ngoc Thanh Nguyen

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© 2015 Springer International Publishing Switzerland

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Maachou, N., Moulaï, M. (2015). Bilevel Quadratic Fractional/Quadratic Problem. In: Le Thi, H., Pham Dinh, T., Nguyen, N. (eds) Modelling, Computation and Optimization in Information Systems and Management Sciences. Advances in Intelligent Systems and Computing, vol 359. Springer, Cham. https://doi.org/10.1007/978-3-319-18161-5_32

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  • DOI: https://doi.org/10.1007/978-3-319-18161-5_32

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18160-8

  • Online ISBN: 978-3-319-18161-5

  • eBook Packages: EngineeringEngineering (R0)

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