A Simplex Approach for Finding Local Solutions of a Linear Bilevel Program by Equilibrium Points

Manoel Campêlo () and Susana Scheimberg

Annals of Operations Research, 2005, vol. 138, issue 1, 143-157

Abstract: In this paper, a linear bilevel programming problem (LBP) is considered. Local optimality conditions are derived. They are based on the notion of equilibrium point of an exact penalization for LBP. It is described how an equilibrium point can be obtained with the simplex method. It is shown that the information in the simplex tableaux can be used to get necessary and sufficient local optimality conditions for LBP. Based on these conditions, a simplex type algorithm is proposed, which attains a local solution of LBP by moving in equilibrium points. A numerical example illustrates how the algorithm works. Some computational results are reported. Copyright Springer Science + Business Media, Inc. 2005

Keywords: bilevel linear programming; local optimization; simplex method (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10479-005-2450-5

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