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

Subject Matter

 * Functional Analysis
 * Calculus of Variations
 * Optimal Control

Contents

 * Preface

Part I: FunctionalAnalysis


 * 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