Management Science and Financial Engineering
- Volume 7 Issue 1
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- Pages.41-56
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- 2001
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- 2287-2043(pISSN)
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- 2287-2361(eISSN)
OPTIMALITY CONDITIONS AND AN ALGORITHM FOR LINEAR-QUADRATIC BILEVEL PROGRAMMING
- Malhotra, Neelam (Department of Mathematics, Hans Raj College, University of Delhi) ;
- Arora, S.R. (Department of Mathematics, Hans Raj College, University of Delhi)
- Published : 2001.05.01
Abstract
This linear fractional - quadratic bilevel programming problem, in which the leader's objective function is a linear fractional function and the follower's objective function is a quadratic function, is studied in this paper. The leader's and the follower's variables are related by linear constraints. The derivations of the optimality conditions are based on Kuhn-Tucker conditions and the duality theory. It is also shown that the original linear fractional - quadratic bilevel programming problem can be solved by solving a standard linear fractional program and the optimal solution of the original problem can be achieved at one of the extreme point of a convex polyhedral formed by the new feasible region. The algorithm is illustrated with the help of an example.
Keywords