Fundamentals of Convex Analysis and Optimization : A Supremum Function Approach / by Rafael Correa, Abderrahim Hantoute, Marco A. López.

Format:

Book

Author/Creator:

Correa, Rafael, 1890- author.

Hantoute, Abderrahim, author.

López, Marco A., author.

Series:

Springer Series in Operations Research and Financial Engineering, 2197-1773

Language:

English

Subjects (All):

Operations research.

Management science.

Mathematical optimization.

Functional analysis.

Operations Research, Management Science.

Optimization.

Functional Analysis.

Local Subjects:

Operations Research, Management Science.

Optimization.

Functional Analysis.

Physical Description:

1 online resource (XIII, 444 p. 1 illus.)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2023.

Summary:

This book aims at an innovative approach within the framework of convex analysis and optimization, based on an in-depth study of the behavior and properties of the supremum of families of convex functions. It presents an original and systematic treatment of convex analysis, covering standard results and improved calculus rules in subdifferential analysis. The tools supplied in the text allow a direct approach to the mathematical foundations of convex optimization, in particular to optimality and duality theory. Other applications in the book concern convexification processes in optimization, non-convex integration of the Fenchel subdifferential, variational characterizations of convexity, and the study of Chebychev sets. At the same time, the underlying geometrical meaning of all the involved concepts and operations is highlighted and duly emphasized. A notable feature of the book is its unifying methodology, as well as the novelty of providing an alternative or complementary view to the traditional one in which the discipline is presented to students and researchers. This textbook can be used for courses on optimization, convex and variational analysis, addressed to graduate and post-graduate students of mathematics, and also students of economics and engineering. It is also oriented to provide specific background for courses on optimal control, data science, operations research, economics (game theory), etc. The book represents a challenging and motivating development for those experts in functional analysis, convex geometry, and any kind of researchers who may be interested in applications of their work.

Contents:

1. Introduction

2. Preliminaries

3. Fenchel-Moreau-Rockafellar theory

4. Fundamental topics in convex analysis

5. Supremum of convex functions

6. The supremum in specific contexts

7. Other subdifferential calculus rules

8. Miscellaneous

9. Exercises - Solutions

Index

Glossary of Notations

Bibliography.

Notes:

Includes bibliographical references and index.

ISBN:

3-031-29551-X