Abstract
We study bilevel optimization problems from the optimistic perspective. The case of one-dimensional leader’s variable is considered. Based on the classification of generalized critical points in one-parametric optimization, we describe the generic structure of the bilevel feasible set. Moreover, optimality conditions for bilevel problems are stated. In the case of higher-dimensional leader’s variable, some bifurcation phenomena are discussed. The links to the singularity theory are elaborated.
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© 2012 Springer Science+Business Media, LLC
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Shikhman, V. (2012). Bilevel Optimization. In: Topological Aspects of Nonsmooth Optimization. Springer Optimization and Its Applications(), vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1897-9_5
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DOI: https://doi.org/10.1007/978-1-4614-1897-9_5
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1896-2
Online ISBN: 978-1-4614-1897-9
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