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Functional analysis and applied optimization in Banach spaces : applications to non-convex variational models /

This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced...

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Bibliographic Details
Main Authors: Botelho, Fábio
Group Author: Ferreira, Anderson; Molter, Alexandre
Published: Springer,
Publisher Address: Cham :
Publication Dates: [2014]
Literature type: Book
Language: English
Subjects:
Functional analysis
Banach spaces
Mathematical optimization
Summary: This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to
Carrier Form: xviii, 560 pages : illustrations (some color) ; 25 cm
Bibliography: Includes bibliographical references (pages 553-555) and index.
ISBN: 9783319060736
3319060732
Index Number: QA320
CLC: O177.2
Call Number: O177.2/B748
Contents: 1. Topological Vector Spaces -- 2. The Hahn-Bananch Theorems and Weak Topologies -- 3. Topics on Linear Operators -- 4. Basic Results on Measure and Integration.-5. The Lebesgue Measure in Rn -- 6. Other Topics in Measure and Integration -- 7. Distributions -- 8. The Lebesque and Sobolev Spaces.-9. Basic Concepts on the Calculus of Variations -- 10. Basic Concepts on Convex Analysis -- 11. Constrained Variational Analysis -- 12. Duality Applied to Elasticity -- 13. Duality Applied to a Plate Model -- 14. About Ginzburg-Landau Type Equations: The Simpler Real Case.-15. Full Complex Ginzburg-L

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