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 reduce point challenge has a specific optimum answer for all parameter values, this challenge is corresponding to a one-level optimization challenge having an implicitly outlined goal functionality. specified emphasize within the e-book is on difficulties having non-unique decrease point optimum options, the confident (or susceptible) and the pessimistic (or powerful) methods are mentioned. The ebook begins with the necessary leads to parametric nonlinear optimization. this can be by means of the most theoretical effects together with worthy and enough optimality stipulations and resolution algorithms for bilevel difficulties. Stationarity stipulations can be utilized to the reduce point challenge to rework the positive bilevel programming challenge right into a one-level challenge. homes 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 learn, and financial modelling. scholars drawn to optimization also will locate this booklet priceless.
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