Subdifferentials: Theory and Applications

Description

Cover Title page Preface Chapter 1. Convex Correspondences and Operators 1. Convex Sets 2. Convex Correspondences 3. Convex Operators 4. Fans and Linear Operators 5. Systems of Convex Objects 6. Comments Chapter 2. Geometry of Subdifferentials 1. The Canonical Operator Method 2. Extremal Structure of Subdifferentials 3. Subdifferentials of Operators Acting in Modules 4. The Intrinsic Structure of Subdifferentials 5. Caps and Faces 6. Comments Chapter 3. Convexity and Openness 1. Openness of Convex Correspondences 2. The Method of General Position 3. Calculus of Polars 4. Dual Characterization of Openness 1 5. Openness and Corn pleteness 6. Comments Chapter 4. The Apparatus of Subdifferential Calculus 1. The Young- Fenchel Transform 2. Formulas for Subdifferentiation 3. Semicontinuity 4. Maharam Operators 5. Disintegration 6. Infinitesimal Subdifferentials 7. Comments Chapter 5. Convex Extremal Problems 1. Vector Programs. Optimality 2. The Lagrange Principle 3. Conditions for Optimality and Approximate Optimality 4. Conditions for Infinitesimal Optimality 5. Existence of Generalized Solutions 6. Comments Chapter 6. Local Convex Approximations 1. Classification of Local Approximations 2. Kuratowski and Rockafellar Limits 3. Approximations Determined by a Set of Infinitesimals 4. Approximation to the Composition of Sets 5. Subdifferentials of Nonsmooth Operators 6. Comments References Author Index Subject Index Symbol Index (missing)