An Optimization Primer

This 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 analysiswould be helpful but is not prerequisite.

Integrates modeling within theoretical developments and computations Focuses on optimization under uncertainty Introduces variational analysis and other advanced subjects Suitable for graduate and advanced undergraduate readership Includes chapter-level exercises

Auteur

Johannes O. Royset, a Professor of Operations Research at the Naval Postgraduate School, is the recipient of the Barchi Prize, the Military OR Journal Award and the Goodeve Medal. He has been a visiting scholar at Stanford University and University of California, Davis as well as an associate editor of SIAM Journal on Optimization, Operations Research and Set-Valued and Variational Analysis. His experience with teaching optimization at the Naval Postgraduate School and University of California, Berkeley extends more than 15 years. He has authored 90 papers and a monograph. Roger J-B Wets, a Distinguished Professor Emeritus of Mathematics at University of California, Davis, has received the G. B. Dantzig Prize in Mathematical Programming, a Pioneer Award for contributions to stochastic optimization and a Doctor Honoris Causa from the University of Vienna. He has been a Guggenheim Fellow as well as editor of SIAM Journal on Control and Optimization and Journal of Convex Analysis. Wets has published more than 200 papers on the theory and application of optimization. His previous book Variational Analysis received the F. W. Lanchester Prize.

Résumé
"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)

Contenu
Prelude.- 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.