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A Study of Local Solutions in Linear Bilevel Programming

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  • M. Campêlo

    (Universidade Federal do Ceará)

  • S. Scheimberg

    (Universidade Federal do Rio de Janeiro)

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.

Suggested Citation

  • M. Campêlo & S. Scheimberg, 2005. "A Study of Local Solutions in Linear Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 63-84, April.
    • Handle: RePEc:spr:joptap:v:125:y:2005:i:1:d:10.1007_s10957-004-1711-9
    DOI: 10.1007/s10957-004-1711-9
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    References listed on IDEAS

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    1. Jonathan F. Bard, 1983. "An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem," Operations Research, INFORMS, vol. 31(4), pages 670-684, August.
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