A Study of Local Solutions in Linear Bilevel Programming

M. Campêlo and S. Scheimberg
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M. Campêlo: Universidade Federal do Ceará
S. Scheimberg: Universidade Federal do Rio de Janeiro

Journal of Optimization Theory and Applications, 2005, vol. 125, issue 1, No 4, 63-84

Abstract: Abstract In this paper, a linear bilevel programming problem (LBP) is considered. Local optimality in LBP is studied via two related problems (P) and P(M). Problem (P) is a one-level model obtained by replacing the innermost problem of LBP by its KKT conditions. Problem P(M) is a penalization of the complementarity constraints of (P) with a penalty parameter M. Characterizations of a (strict) local solution of LBP are derived. In particular, the concept of equilibrium point of P(M) is used to characterize the local optima of (P) and LBP.

Keywords: Bilevel linear programming; local optimization; exact penalty methods; equilibrium constraints (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-1711-9

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