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

Sanjeet Singh () and Nivedita Haldar ()
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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

International Game Theory Review (IGTR), 2015, vol. 17, issue 02, 1-18

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.

Keywords: Bi-level programming; stackelberg game; quadratic programming; linear fractional programming; dual problem; quadratic linear fractional problem; 90B50; 90C20; 90C32 (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1142/S0219198915400174

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