Carlier G. Classical And Modern Optimization 2022

Textbook in PDF format

The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning. Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications. Valuable to a wide audience, including students in mathematics, engineers, data scientists or economists, Classical and Modern Optimization contains more than 200 exercises to assist with self-study or for anyone teaching a third- or fourth-year optimization class.
Preface.
About the Author.
Topological and Functional Analytic Preliminaries.
Differential Calculus.
Convexity.
Optimality Conditions for Differentiable Optimization.
Problems Depending on a Parameter.
Convex Duality and Applications.
Iterative Methods for Convex Minimization.
When Optimization and Data Meet.
An Invitation to the Calculus of Variations.
Bibliography.
Index