This article is cited in 15 papers

Numerical solution of a linear bilevel problem

T. V. Gruzdeva, E. G. Petrova

Institute of Dynamical Systems and Control Theory, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033 Russia

Abstract: The linear bilevel programming problem in the optimistic formulation is studied. It is reduced to an optimization problem with a nonconvex constraint in the form of a d.c. function (that is, the difference of two convex functions). For this problem, local and global search methods are developed. Numerical experiments performed for numerous specially generated problems, including large-scale ones, demonstrate the efficiency of the proposed approach.

Key words: linear bilevel problem, optimistic solution, problem with d.c. inequality, local search, global search, numerical experiment.

UDC: 519.626

Received: 05.02.2010
Revised: 13.05.2010

 English version: Computational Mathematics and Mathematical Physics, 2010, 50:10, 1631–1641

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