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.

Guillaume Carlier is Professor of Mathematics at Université Paris-Dauphine and a member of the joint research team Mokaplan between INRIA Paris and Dauphine. He co-authored more than 100 research articles in various fields such as optimal transport, calculus of variations, mathematical economics, partial differential equations, cities modelling, etc. He also belongs to the editorial board of several journals (Journal de l'École Polytechnique, Applied Mathematics and Optimization, Journal of Mathematical Analysis and Applications, Mathematics and Financial Economics and Journal of Dynamics and Games).