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A New Method To Solve Bi-Level Quadratic Linear Fractional Programming Problems

Author

Listed:
  • Sanjeet Singh

    (Operations Management Group, Indian Institute of Management Calcutta, DH Road, Joka, Kolkata-700104, India)

  • Nivedita Haldar

    (Operations Management Group, Indian Institute of Management Calcutta, DH Road, Joka, Kolkata-700104, India)

Abstract

In this paper, we have developed a new method to solve bi-level quadratic linear fractional programming (BLQLFP) problems in which the upper-level objective function is quadratic and the lower-level objective function is linear fractional. In this method a BLQLFP problem is transformed into an equivalent single-level quadratic programming (QP) problem with linear constraints by forcing the duality gap of the lower-level problem to zero. Then by obtaining all vertices of the constraint region of the dual of the lower-level problem, which is a convex polyhedron, the single-level QP problem is converted into a series of finite number of QP problems with linear constraints which can be solved by any standard method for solving a QP. The best among the optimal solutions gives the desired optimal solution for the original bi-level programming (BLP) problem. Theoretical results have been illustrated with the help of a numerical example.

Suggested Citation

  • Sanjeet Singh & Nivedita Haldar, 2015. "A New Method To Solve Bi-Level Quadratic Linear Fractional Programming Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-18.
    • Handle: RePEc:wsi:igtrxx:v:17:y:2015:i:02:n:s0219198915400174
    DOI: 10.1142/S0219198915400174
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    Keywords

    Bi-level programming; stackelberg game; quadratic programming; linear fractional programming; dual problem; quadratic linear fractional problem; 90B50; 90C20; 90C32;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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