Description
Book SynopsisThis richly illustrated book introduces the subject of optimization to a broad audience with a balanced treatment of theory, models and algorithms. Through numerous examples from statistical learning, operations research, engineering, finance and economics, the text explains how to formulate and justify models while accounting for real-world considerations such as data uncertainty. It goes beyond the classical topics of linear, nonlinear and convex programming and deals with nonconvex and nonsmooth problems as well as games, generalized equations and stochastic optimization.
The book teaches theoretical aspects in the context of concrete problems, which makes it an accessible onramp to variational analysis, integral functions and approximation theory. More than 100 exercises and 200 fully developed examples illustrate the application of the concepts. Readers should have some foundation in differential calculus and linear algebra. Exposure to real analysis would be helpful but is not prerequisite.
Trade Review“In the reviewer's opinion, this is an important book … . a lot of applications are given, so on one hand the readers can benefit from deep insights into the mathematical background of optimization theory … . This book, which as all books reflects the tastes of its authors, is a solid reference, not only for graduate students and postgraduate students, but also for all those researchers interested in recent developments of optimization theory and methods.” (Giorgio Giorgi, Mathematical Reviews, December, 2022)
Table of ContentsPrelude.- Convex optimization.- Optimization under uncertainty.- Minimization problems.- Perturbation and duality.- Without convexity or smoothness.- Generalized Equations.- Risk modeling and sample averages.- Games and minsup problems.- Decomposition.
