Classical and modern optimization
- New Jersey : World Scientific, 2022
- xiii, 371 p.; ill., 23 cm
- Advanced textbooks in mathematics .
Includes bibliographical references and index.
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.
9781944660529
Mathematical optimization Functional Analysis Banach space Baire's theorem Dunford-Pettis theorem Envelope t5heorem Fenchel-Rockafellar theorem Green formula Hopf-Lax formula Inverse function theorem Krein-Milman theorem Lax-Oleinik formula Minkowski Farkes theorem Newton's law Rademacher's theorem Strong linear programming (LP) duality theorem