Download PDF by Stephan Dempe: Foundations of bilevel programming

By Stephan Dempe

ISBN-10: 1441952209

ISBN-13: 9781441952202

Bilevel programming difficulties are hierarchical optimization difficulties the place the restrictions of 1 challenge (the so-called higher point challenge) are outlined partly by way of a moment parametric optimization challenge (the decrease point problem). If the reduce point challenge has a special optimum resolution for all parameter values, this challenge is such as a one-level optimization challenge having an implicitly outlined aim functionality. exact emphasize within the ebook is on difficulties having non-unique reduce point optimum ideas, the positive (or vulnerable) and the pessimistic (or robust) methods are mentioned. The publication starts off with the necessary ends up in parametric nonlinear optimization. this can be via the most theoretical effects together with worthy and enough optimality stipulations and resolution algorithms for bilevel difficulties. Stationarity stipulations may be utilized to the reduce 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 homes, 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 monetary modelling. scholars drawn to optimization also will locate this ebook priceless.

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Extra info for Foundations of bilevel programming

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2 TWO-DIMENSIONAL CONVEX REGIONS We begin by giving some simple examples of convex regions. 5) consists of a region in two-dimensional space on one side of the line (see Figure 1-2): x1 + x2 = 2. 6) This is an example of a convex region, or, what is the same thing, a convex set of points. The region defined by the shaded area between two vectors indefinitely extended (see Figure 1-2) is also a convex set. Various other examples of convex regions in two dimensions can be constructed.

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Foundations of bilevel programming by Stephan Dempe


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