凸・確率的最適化（テキスト） Convex and Stochastic Optimization (Universitext)

Bonnans, J. Frédéric

Springer Nature Switzerland AG（2019/04発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 311 p.
• 商品コード 9783030149765

Full Description

This textbook provides an introduction to convex duality for optimization problems in Banach spaces, integration theory, and their application to stochastic programming problems in a static or dynamic setting. It introduces and analyses the main algorithms for stochastic programs, while the theoretical aspects are carefully dealt with.

The reader is shown how these tools can be applied to various fields, including approximation theory, semidefinite and second-order cone programming and linear decision rules.

This textbook is recommended for students, engineers and researchers who are willing to take a rigorous approach to the mathematics involved in the application of duality theory to optimization with uncertainty.

Contents

1 A convex optimization toolbox.- 2 Semidefinite and semiinfinite programming.- 3 An integration toolbox.- 4 Risk measures.- 5 Sampling and optimizing.- 6 Dynamic stochastic optimization.- 7 Markov decision processes.- 8 Algorithms.- 9 Generalized convexity and transportation theory.- References.- Index.