Preface
List of Figures
0 Introduction
1 Analysis Without Lineaxization
2 Flow-Invariant Sets
3 Optimization
4 Control Theory
5 Notation
1 Proximal Calculus in Hilbert Space
1 Closest Points and Proximal Normals
2 Proximal Subgradients
3 The Density Theorem
4 Minimization Principles
5 Quadratic Inf-Convolutions
6 The Distance Function
7 Lipschitz Functions
8 The Sum Rule
9 The Chain Rule
10 Limiting Calculus
11 Problems on Chapter 1
2 Generalized Gradients in Banach Space
1 Definition and Basic Properties
2 Basic Calculus
3 Relation to Derivatives
4 Convex and Regular Functions
5 Tangents and Normals
6 Relationship to Proximal Analysis
7 The Bouligand Tangent Cone and Regular Sets
8 The Gradient Formula in Finite Dimensions
9 Problems on Chapter 2
3 Special Topics
1 Constrained Optimization and Value Functions
2 The Mean Value Inequality
3 Solving Equations
4 Derivate Calculus and Rademachers Theorem
5 Sets in L2 and Integral b-~~nctionals
6 Tangents and Interiors
7 Problems on Chapter 3
4 A Short Course in Control Theory
1 Trajectories of DiffercntiM Inclusions
2 Weak Invariance
3 Lipschitz Dependence and Strong Invariance
4 Equilibria
5 Lyapounov Theory and Stabilization
6 Monotonicity and Attainability
7 The Hamilton Jacobi Equation and Viscosity Solutions
8 Feedback Synthesis from Semisolutions
9 Necessary Conditions for Optimal Control
10 Normality and Controllability
11 Problems on Chapter 4
Notes and Comments
List of Notation
Bibliography
Index
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