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Chapter 1．Max and Min1

A．Penalties and Constraints2

B．Epigraphs and Semicontinuity7

C．Attainment of a Minimum11

D．Continuity,Closure and Growth13

E．Extended Arithmetic15

F．Parametric Dependence16

G．Moreau Envelopes20

H．Epi-Addition and Epi-Multiplication23

I．Auxiliary Facts and Principles28

Commentary34

Chapter 2．Convexity38

A．Convex Sets and Functions38

B．Level Sets and Intersections42

C．Derivative Tests45

D．Convexity in Operations49

E．Convex Hulls53

F．Closures and Continuity57

G．Separation62

H．Relative Interiors64

I．Piecewise Linear Functions67

J．Other Examples71

Commentary74

Chapter 3．Cones and Cosmic Closure77

A．Direction Points77

B．Horizon Cones80

C．Horizon Functions86

D．Coercivity Properties90

E．Cones and Orderings95

F．Cosmic Convexity97

G．Positive Hulls99

Commentary105

Chapter 4．Set Convergence108

A．Inner and Outer Limits109

B．Painlevé-Kuratowski Convergence111

C．Pompeiu-Hausdorff Distance117

D．Cones and Convex Sets118

E．Compactness Properties120

F．Horizon Limits122

G．Continuity of Operations125

H．Quantification of Convergence131

I．Hyperspace Metrics138

Commentary144

Chapter 5．Set-Valued Mappings148

A．Domains,Ranges and Inverses149

B．Continuity and Semicontinuity152

C．Local Boundedness157

D．Total Continuity164

E．Pointwise and Graphical Convergence166

F．Equicontinuity of Sequences173

G．Continuons and Uniform Convergence175

H．Metric Descriptions of Convergence181

I．Operations on Mappings183

J．Generic Continuity and Selections187

Commentary192

Chapter 6．Variational Geometry196

A．Tangent Cones196

B．Normal Cones and Clarke Regularity199

C．Smooth Manifolds and Convex Sets202

D．Optimality and Lagrange Multipliers205

E．Proximal Normals and Polarity212

F．Tangent-Normal Relations217

G．Recession Properties222

H．Irregularity and Convexification225

I．Other Formulas227

Commentary232

Chapter 7．Epigraphical Limits238

A．Pointwise Convergence239

B．Epi-Convergence240

C．Continuous and Uniform Convergence250

D．Generalized Differentiability255

E．Convergence in Minimization262

F．Epi-Continuity of Function-Valued Mappings269

G．Continuity of Operations275

H．Total Epi-Convergence278

I．Epi-Distances282

J．Solution Estimates286

Commentary292

Chapter 8．Subderivatives and Subgradients298

A．Subderivatives of Functions299

B．Subgradients of Functions300

C．Convexity and Optimality308

D．Regular Subderivatives311

E．Support Functions and Subdifierential Duality317

F．Calmness322

G．Graphical Differentiation of Mappings324

H．Proto-Differentiability and Graphical Regularity329

I．Proximal Subgradients333

J．Other Results336

Commentary343

Chapter 9．Lipschitzian Properties349

A．Single-Valued Mappings349

B．Estimates of the Lipschitz Modulus354

C．Subdifferential Characterizations358

D．Derivative Mappings and Their Norms364

E．Lipschitzian Concepts for Set-Valued Mappings368

F．Aubin Property and Mordukhovich Criterion376

G．Metric Regularity and Openness386

H．Semiderivatives and Strict Graphical Derivatives390

I．Other Properties399

J．Rademacher's Theorem and Consequences403

K．Mollifiers and Extremals408

Commentary415

Chapter 10．Subdifferential Calculus421

A．Optimality and Normals to Level Sets421

B．Basic Chain Rule426

C．Parametric Optimality432

D．Rescaling438

E．Piecewise Linear-Quadratic Functions440

F．Amenable Sets and Functions442

G．Semiderivatives and Subsmoothness446

H．Coderivative Calculus452

I．Extensions458

Commentary469

Chapter 11．Dualization473

A．Legendre-Fenchel Transform473

B．Special Cases of Conjugacy476

C．The Role of Differentiability480

D．Piecewise Linear-Quadratic Functions484

E．Polar Sets and Gauges490

F．Dual Operations493

G．Duality in Convergence500

H．Dual Problems of Optimization502

I．Lagrangian Functions508

J．Minimax Problems514

K．Augmented Lagrangians and Nonconvex Duality518

L．Generalized Conjugacy525

Commentary529

Chapter 12．Monotone Mappings533

A．Monotonicity Tests and Maximality533

B．Minty Parameterization537

C．Connections with Convex Functions542

D．Graphical Convergence551

E．Domains and Ranges553

F．Preservation of Maximality556

G．Monotone Variational Inequalities559

H．Strong Monotonicity and Strong Convexity562

I．Continuity and Differentiability567

Commentary575

Chapter 13．Second-Order Theory579

A．Second-Order Differentiability579

B．Second Subderivatives582

C．Calculus Rules591

D．Convex Functions and Duality603

E．Second-Order Optimality606

F．Prox-Regularity609

G．Subgradient Proto-Differentiability618

H．Subgradient Coderivatives and Perturbation622

I．Further Derivative Properties625

J．Parabolic Subderivatives633

Commentary638

Chapter 14．Measurability642

A．Measurable Mappings and Selections643

B．Preservation of Measurability651

C．Limit Operations655

D．Normal Integrands660

E．Operations on Integrands669

F．Integral Functionals675

Commentary679

References684

Index of Statements710

Index of Notation725

Index of Topics726