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

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

Contents

Preface

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

References

Index