最適化入門（テキスト） An Optimization Primer (Springer Series in Operations Research and Financial Engineering)

Royset, Johannes O./ Wets, Roger J-B

Springer Nature Switzerland AG（2023/03発売）

Springer Nature Switzerland AG（2023/03発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 676 p.
• 言語 ENG
• 商品コード 9783030762773

Full Description

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. 

Contents

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.