Functional Analysis Calculus of Variations and Optimal Control 1st edition by Francis Clarke – Ebook PDF Instant Download/Delivery: 1447148193, 978-1447148197
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ISBN 10: 1447148193
ISBN 13: 978-1447148197
Author: Francis Clarke
Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor.
This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Othermajor themes include existence and Hamilton-Jacobi methods.
The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering.
Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.
Functional Analysis Calculus of Variations and Optimal Control 1st Table of contents:
1. Functional Analysis
2. Convex sets and functions
3. Weak topologies
4. Convex analysis
5. Banach spaces
6. Lebesgue spaces
7. Hilbert spaces
8. Additional exercises for Part I
2. Optimization and Nonsmooth Analysis
10. Generalized gradients
11. Proximal analysis
12. Invariance and monotonicity
13. Additional exercises for Part II
3. Calculus of Variations
15. Nonsmooth extremals
16. Absolutely continuous solutions
17. The multiplier rule
18. Nonsmooth Lagrangians
19. Hamilton-Jacobi methods
20. Multiple integrals
21. Additional exercises for Part III
4. Optimal Control
23. Existence and regularity
24. Inductive methods
25. Differential inclusions
26. Additional exercises for Part IV
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