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. Sample Chapter(s) Preface Chapter 1: Topological and Functional Analytic Preliminaries Request Inspection Copy Contents: Topological and Functional Analytic Preliminaries: Metric Spaces Normed Vector Spaces Banach Spaces Hilbert Spaces Weak Convergence On the Existence and Generic Uniqueness of Minimizers Exercises Differential Calculus: First-Order Differential Calculus Second-Order Differential Calculus The Inverse Function and Implicit Function Theorems Smooth Functions on ℝd, Regularization, Integration by Parts Exercises Convexity: Hahn–Banach Theorems Convex Sets Convex Functions The Legendre Transform Exercises Optimality Conditions for Differentiable Optimization: Unconstrained Optimization Equality Constraints Equality and Inequality Constraints Exercises Problems Depending on a Parameter: Setting and Examples Continuous Dependence Parameter-Independent Constraints, Envelope Theorems Parameter-Dependent Constraints Discrete-Time Dynamic Programming Exercises Convex Duality and Applications: Generalities Convex Duality with Respect to a Perturbation Applications On the Optimal Transport Problem Exercises Iterative Methods for Convex Minimization: On Newton's Method The Gradient Method The Proximal Point Method Splitting Methods Exercises When Optimization and Data Meet: Principal Component Analysis Minimization for Linear Systems Classification Exercises An Invitation to the Calculus of Variations: Preliminaries On Integral Functionals The Direct Method Euler–Lagrange Equations and Other Necessary Conditions A Focus on the Case d = 1 Exercises Readership: Thought-leaders, executives, industry strategists, research scientists, graduate students, advanced undergraduate students, policy-makers, research funding agencies, private research institutions, government regulators, investors, corporate managers, purchasing agents, and entrepreneurs in the areas of computer science, quantum computing, information theory, neuroscience, and physics.