| Introduction | p. 1 |
| Preliminaries | p. 5 |
| Terminology | p. 5 |
| Convex Sets in Normed Vector Spaces | p. 6 |
| Convex Functionals: Definitions and Examples | p. 8 |
| Continuity of Convex Functionals | p. 11 |
| Sandwich and Separation Theorems | p. 13 |
| Dual Pairs of Vector Spaces | p. 19 |
| Lower Semicontinuous Functionals | p. 22 |
| Bibliographical Notes and Exercises | p. 24 |
| The Conjugate of Convex Functionals | p. 27 |
| The Gamma Regularization | p. 27 |
| Conjugate Functionals | p. 29 |
| A Theorem of Hörmander and the Bipolar Theorem | p. 34 |
| The Generalized Farkas Lemma | p. 36 |
| Bibliographical Notes and Exercises | p. 38 |
| Classical Derivatives | p. 39 |
| Directional Derivatives | p. 39 |
| First-Order Derivatives | p. 41 |
| Mean Value Theorems | p. 44 |
| Relationship between Differentiability Properties | p. 46 |
| Higher-Order Derivatives | p. 48 |
| Some Examples | p. 49 |
| Implicit Function Theorems and Related Results | p. 51 |
| Bibliographical Notes and Exercises | p. 57 |
| The Subdifferential of Convex Functionals | p. 59 |
| Definition and First Properties | p. 59 |
| Multifunctions: First Properties | p. 63 |
| Subdifferentials, Fréchet Derivatives, and Asplund Spaces | p. 64 |
| Subdifferentials and Conjugate Functionals | p. 73 |
| Further Calculus Rules | p. 76 |
| The Subdifferential of the Norm | p. 78 |
| Differentiable Norms | p. 83 |
| Bibliographical Notes and Exercises | p. 89 |
| Optimality Conditions for Convex Problems | p. 91 |
| Basic Optimality Conditions | p. 91 |
| Optimality Under Functional Constraints | p. 92 |
| Application to Approximation Theory | p. 96 |
| Existence of Minimum Points and the Ritz Method | p. 99 |
| Application to Boundary Value Problems | p. 105 |
| Bibliographical Notes and Exercises | p. 110 |
| Duality of Convex Problems | p. 111 |
| Duality in Terms of a Lagrange Function | p. 111 |
| Lagrange Duality and Gâteaux Differentiable Functionals | p. 116 |
| Duality of Boundary Value Problems | p. 118 |
| Duality in Terms of Conjugate Functions | p. 122 |
| Bibliographical Notes and Exercises | p. 129 |
| Derivatives and Subdifferentials of Lipschitz Functionals | p. 131 |
| Preview: Derivatives and Approximating Cones | p. 131 |
| Upper Convex Approximations and Locally Convex Functionals | p. 135 |
| The Subdifferentials of Clarke and Michel-Penot | p. 139 |
| Subdifferential Calculus | p. 146 |
| Bibliographical Notes and Exercises | p. 153 |
| Variational Principles | p. 155 |
| Introduction | p. 155 |
| The Loewen-Wang Variational Principle | p. 156 |
| TheBorwein-Preiss Variational Principle | p. 161 |
| The Deville-Godefroy-Zizler Variational Principle | p. 162 |
| Bibliographical Notes and Exercises | p. 166 |
| Subdifferentials of Lower Semicontinuous Functionals | p. 167 |
| Fréchet Subdifferentials: First Properties | p. 167 |
| Approximate Sum and Chain Rules | p. 172 |
| Application to Hamilton-Jacobi Equations | p. 181 |
| An Approximate Mean Value Theorem | p. 182 |
| Fréchet Subdifferential vs. Clarke Subdifferential | p. 184 |
| Multidirectional Mean Value Theorems | p. 185 |
| The Fréchet Subdifferential of Marginal Functions | p. 190 |
| Bibliographical Notes and Exercises | p. 193 |
| Multifunctions | p. 195 |
| The Generalized Open Mapping Theorem | p. 195 |
| Systems of Convex Inequalities | p. 197 |
| Metric Regularity and Linear Openness | p. 200 |
| Openness Bounds of Multifunctions | p. 209 |
| Weak Metric Regularity and Pseudo-Lipschitz Continuity | p. 211 |
| Linear Semiopenness and Related Properties | p. 213 |
| Linearly Semiopen Processes | p. 217 |
| Maximal Monotone Multifunctions | p. 219 |
| Convergence of Sets | p. 225 |
| Bibliographical Notes and Exercises | p. 227 |
| Tangent and Normal Cones | p. 231 |
| Tangent Cones: First Properties | p. 231 |
| Normal Cones: First Properties | p. 237 |
| Tangent and Normal Cones to Epigraphs | p. 241 |
| Representation of Tangent Cones | p. 245 |
| Contingent Derivatives and a Lyusternik Type Theorem | p. 252 |
| Representation of Normal Cones | p. 255 |
| Bibliographical Notes and Exercises | p. 261 |
| Optimality Conditions for Nonconvex Problems | p. 265 |
| Basic Optimality Conditions | p. 265 |
| Application to the Calculus of Variations | p. 267 |
| Multiplier Rules Involving Upper Convex Approximations | p. 272 |
| Clarke's Multiplier Rule | p. 278 |
| Approximate Multiplier Rules | p. 280 |
| Bibliographical Notes and Exercises | p. 283 |
| Extremal Principles and More Normals and Subdifferentials | p. 285 |
| Mordukhovich Normals and Subdifferentials | p. 285 |
| Coderivatives | p. 294 |
| Extremal Principles Involving Translations | p. 301 |
| Sequentially Normally Compact Sets | p. 309 |
| Calculus for Mordukhovich Subdifferentials | p. 315 |
| Calculus for Mordukhovich Normals | p. 320 |
| Optimality Conditions | p. 323 |
| The Mordukhovich Subdifferential of Marginal Functions | p. 327 |
| A Nonsmooth Implicit Function Theorem | p. 330 |
| An Implicit Multifunction Theorem | p. 334 |
| An Extremal Principle Involving Deformations | p. 337 |
| Application to Multiobjective Optimization | p. 340 |
| Bibliographical Notes and Exercises | p. 343 |
| Appendix: Further Topics | p. 347 |
| References | p. 351 |
| Notation | p. 363 |
| Index | p. 366 |
| Table of Contents provided by Publisher. All Rights Reserved. |
