By Stephan Dempe
Bilevel programming difficulties are hierarchical optimization difficulties the place the restrictions of 1 challenge (the so-called top point challenge) are outlined partially through a moment parametric optimization challenge (the decrease point problem). If the decrease point challenge has a precise optimum resolution for all parameter values, this challenge is such as a one-level optimization challenge having an implicitly outlined target functionality. exact emphasize within the ebook is on difficulties having non-unique decrease point optimum strategies, the positive (or vulnerable) and the pessimistic (or robust) ways are mentioned. The publication begins with the necessary leads to parametric nonlinear optimization. this is often via the most theoretical effects together with invaluable and enough optimality stipulations and answer algorithms for bilevel difficulties. Stationarity stipulations can be utilized to the reduce point challenge to remodel the confident 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 examine, and monetary modelling. scholars drawn to optimization also will locate this e-book beneficial.
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