Convex Analysis in General Vector Spaces

The following sections are included:

• Preface

• Contents

• Introduction

The following sections are included:

• Preliminary Notions and Results

• Closedness and Interiority Notions

• Open Mapping Theorems

• Variational Principles

• Exercises

• Bibliographical Notes

The following sections are included:

• Convex Functions

• Semi-Continuity of Convex Functions

• Conjugate Functions

• The Subdifferential of a Convex Function

• The General Problem of Convex Programming

• Perturbed Problems

• The Fundamental Duality Formula

• Formulas for Conjugates and ε-Subdifferentials, Duality Relations and Optimality Conditions

• Convex Optimization with Constraints

• A Minimax Theorem

• Exercises

• Bibliographical Notes

The following sections are included:

• Further Fundamental Results in Convex Analysis

• Convexity and Monotonicity of Subdifferentials

• Some Classes of Functions of a Real Variable and Differentiability of Convex Functions

• Well Conditioned Functions

• Uniformly Convex and Uniformly Smooth Convex Functions

• Uniformly Convex and Uniformly Smooth Convex Functions on Bounded Sets

• Applications to the Geometry of Normed Spaces

• Applications to the Best Approximation Problem

• Characterizations of Convexity in Terms of Smoothness

• Weak Sharp Minima, Well-behaved Functions and Global Error Bounds for Convex Inequalities

• Monotone Multifunctions

• Exercises

• Bibliographical Notes

The following sections are included:

• Exercises – Solutions

• Bibliography

• Index

• Symbols and Notations