On bilevel programming, Part I: General nonlinear cases

On bilevel programming, Part I: General nonlinear cases

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Article ID: iaor19971122
Country: Netherlands
Volume: 70
Issue: 1
Start Page Number: 47
End Page Number: 72
Publication Date: Oct 1995
Journal: Mathematical Programming (Series A)
Authors: ,
Keywords: bilevel optimization
Abstract:

This paper is concerned with general nonlinear nonconvex bilevel programming problems (BLPP). The authors derive necessary and sufficient conditions at a local solution and investigate the stability and sensitivity analysis at a local solution in the BLPP. They then explore an approach in which a bundle method is used in the upper-level problem with subgradient information from the lower-level problem. Two algorithms are proposed to solve the general nonlinear BLPP and are shown to converge to regular points of the BLPP under appropriate conditions. The theoretical analysis conducted in this paper seems to indicate that a sensitivity-based approach is rather promising for solving general nonlinear BLPP.

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