Book:Francis Clarke/Functional Analysis, Calculus of Variations and Optimal Control

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Francis Clarke: Functional Analysis, Calculus of Variations and Optimal Control

Published $\text {2013}$, Springer

ISBN 978-1-4471-4819-7

Subject Matter

Functional Analysis
Calculus of Variations
Optimal Control



Part I: Functional Analysis

1 Normed Spaces
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

Part II: Optimization and Nonsmooth Analysis

9 Optimization and multipliers
10 Generalized gradients
11 Proximal analysis
12 Invariance and monotonicity
13 Additional exercises for Part II

Part III: Calculus of Variations

14 The classical theory
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

Part IV: Optimal Control

22 Necessary conditions
23 Existence and regularity
24 Inductive methods
25 Differentia linclusions
26 Additional exercises for Part IV

Notes, solutions, and hints