Fermat Days 85 Mathematics For Optimization

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Author: J.-B. Hiriart-Urruty
Publisher: Elsevier
ISBN: 9780080872407
Size: 44.40 MB
Format: PDF, Kindle
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Fermat Days 85 Mathematics For Optimization by J.-B. Hiriart-Urruty


Original Title: Fermat Days 85 Mathematics For Optimization

Optimization, as examined here, ranges from differential equations to problems arising in Mechanics and Statistics. The main topics covered are: calculations of variations and nonlinear elasticity, optimal control, analysis and optimization in problems dealing with nondifferentiable data, duality techniques, algorithms in mathematical programming and optimal control.

Topologies On Closed And Closed Convex Sets

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Author: Gerald Beer
Publisher: Springer Science & Business Media
ISBN: 9780792325314
Size: 22.53 MB
Format: PDF
View: 5451

Topologies On Closed And Closed Convex Sets by Gerald Beer


Original Title: Topologies On Closed And Closed Convex Sets

This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well. A unifying theme is the relationship between topology and set convergence on the one hand, and set functionals on the other. The text includes for the first time anywhere an exposition of three topologies that over the past ten years have become fundamental tools in optimization, one-sided analysis, convex analysis, and the theory of multifunctions: the Wijsman topology, the Attouch--Wets topology, and the slice topology. Particular attention is given to topologies on lower semicontinuous functions, especially lower semicontinuous convex functions, as associated with their epigraphs. The interplay between convex duality and topology is carefully considered and a chapter on set-valued functions is included. The book contains over 350 exercises and is suitable as a graduate text. This book is of interest to those working in general topology, set-valued analysis, geometric functional analysis, optimization, convex analysis and mathematical economics.

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