Download Foundations of Bilevel Programming (Nonconvex Optimization by Stephan Dempe PDF

By Stephan Dempe

Bilevel programming difficulties are hierarchical optimization difficulties the place the limitations of 1 challenge (the so-called higher point challenge) are outlined partly by way of a moment parametric optimization challenge (the reduce point problem). If the decrease point challenge has a exact optimum answer for all parameter values, this challenge is comparable to a one-level optimization challenge having an implicitly outlined aim functionality. designated emphasize within the publication is on difficulties having non-unique decrease point optimum suggestions, the positive (or vulnerable) and the pessimistic (or robust) methods are mentioned. The ebook begins with the necessary ends up in parametric nonlinear optimization. this can be via the most theoretical effects together with valuable and enough optimality stipulations and answer algorithms for bilevel difficulties. Stationarity stipulations can be utilized to the decrease point challenge to remodel the positive bilevel programming challenge right into a one-level challenge. houses of the ensuing challenge are highlighted and its relation to the bilevel challenge is investigated. balance houses, numerical complexity, and difficulties having extra integrality stipulations at the variables also are discussed.
Audience: utilized mathematicians and economists operating in optimization, operations study, and fiscal modelling. scholars attracted to optimization also will locate this e-book useful.

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