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

Autorentext

Dr. Stone is Chief Scientist at Metron Inc. He is a member of the National Academy of Engineering and a fellow of the Institute for Operations Research and Management Science. In 1975, the Operations Research Society of America awarded the Lanchester Prize to Dr. Stone's text, Theory of Optimal Search. In 1986, he produced the probability maps used to locate the S.S. Central America which sank in 1857, taking millions of dollars of gold coins and bars to the ocean bottom one and one-half miles below. In 2010 he led the team that produced the probability distribution that guided the French to the location of the underwater wreckage of Air France Flight AF447. He is a coauthor of the 2014 book, Bayesian Multiple Target Tracking. He continues to work on a number of detection and tracking systems for the United States Navy and Coast Guard including the Search And Rescue Optimal Planning System used by the Coast Guard since 2007to plan searches for people missing at sea. Dr. Johannes O. Royset is Associate Chair of Research and Associate Professor of Operations Research at the Naval Postgraduate School. Dr. Royset's research focuses on formulating and solving stochastic and deterministic optimization problems arising in data analysis, sensor management, and reliability engineering. Dr. Royset has a Doctor of Philosophy degree from the University of California at Berkeley (2002). He was awarded a National Research Council postdoctoral fellowship in 2003, a Young Investigator Award from the Air Force Office of Scientific Research in 2007, and the Barchi Prize as well as the MOR Journal Award from the Military Operations Research Society in 2009. He received the Carl E. and Jessie W. Menneken Faculty Award for Excellence in Scientific Research in 2010. Dr. Royset is an associate editor of Operations Research, Naval Research Logistics, Journal of Optimization Theory and Applications, and Computational Optimization and Applications. Alan Washburn received a Ph. D. in Electrical Engineering from Carnegie Institute of Technology in 1965, and has been with the Operations Research Department at the Naval Postgraduate School since 1970. He is a member of the National Academy of Engineering, and is the recipient of several awards and prizes, including the Distinguished Civilian Service Award for his research and tutorial notes on several topics of importance to the Department of Defense. He is the author of over 50 scientific publications, including several books. His research is almost entirely military, emphasizing problems that employ search theory, game theory or both. He is a member of INFORMS and also of the Military Operations Research Society (MORS).

Inhalt
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.