Fundamentals of Convex Analysis and Optimization: A Supremum Function Approach

Preface
Contents
1 Introduction
	1.1 Motivation
	1.2 Historical antecedents
	1.3 Working framework and objectives
2 Preliminaries
	2.1 Functional analysis background
	2.2 Convexity and continuity
	2.3 Examples of convex functions
	2.4 Exercises
	2.5 Bibliographical notes
3 Fenchel–Moreau–Rockafellar theory
	3.1 Conjugation theory
	3.2 Fenchel–Moreau–Rockafellar theorem
	3.3 Dual representations of support …
	3.4 Minimax theory
	3.5 Exercises
	3.6 Bibliographical notes
4 Fundamental topics in convex analysis
	4.1 Subdifferential theory
	4.2 Convex duality
	4.3 Convexity in Banach spaces
	4.4 Subdifferential integration
	4.5 Exercises
	4.6 Bibliographical notes
5 Supremum of convex functions
	5.1 Conjugacy-based approach
	5.2 Main subdifferential formulas
	5.3 The role of continuity assumptions
	5.4 Exercises
	5.5 Bibliographical notes
6 The supremum in specific contexts
	6.1 The compact-continuous setting
	6.2 Compactification approach
	6.3 Main subdifferential formula …
	6.4 Homogeneous formulas
	6.5 Qualification conditions
	6.6 Exercises
	6.7 Bibliographical notes
7 Other subdifferential calculus rules
	7.1 Subdifferential of the sum
	7.2 Symmetric versus asymmetric …
	7.3 Supremum-sum subdifferential …
	7.4 Exercises
	7.5 Bibliographical notes
8 Miscellaneous
	8.1 Convex systems and Farkas-type …
	8.2 Optimality and duality in …
	8.3 Convexification processes in …
	8.4 Non-convex integration
	8.5 Variational characterization of …
	8.6 Chebychev sets and convexity
	8.7 Exercises
	8.8 Bibliographical notes
9 Exercises - Solutions
	9.1 Exercises of chapter 2摥映數爠eflinkchone22
	9.2 Exercises of chapter 3摥映數爠eflinkch2a33
	9.3 Exercises of chapter 4摥映數爠eflinkch2b44
	9.4 Exercises of chapter 5摥映數爠eflinkch355
	9.5 Exercises of chapter 6摥映數爠eflinkch4a66
	9.6 Exercises of chapter 7摥映數爠eflinkch477
	9.7 Exercises of chapter 8摥映數爠eflinkch688
Appendix  Glossary of notations
Appendix  Bibliography
Index