- Provides a pedagogical, self-contained analysis of the theory of convex optimization and stochastic programming
- Offers a synthetical view of many applications such as semidefinite programming, Markov processes, generalized convexity and optimal transport
- Includes a study of algorithmic aspects: dynamic programming, stochastic dual dynamic programming (in the case of convex Bellman value functions) and linear decision rules
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- About this Textbook
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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.
- About the authors
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J.F. Bonnans is an expert in convex analysis and dynamic optimization, both in the deterministic and stochastic setting. His main contributions deal with the sensitivity analysis of optimization problems, high order optimality conditions, optimal control and stochastic control. He worked on quantization methods for stochastic programming problems, on the approximate dynamic programming for problems with monotone value function, and on sparse linear regression.
- Reviews
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“The book is mainly devoted to the theoretical study of concepts of stochastic programming. … The book offers a solid theoretical background for researchers/students/practitioners keen on disposing of a rigorous foundation of stochastic programming.” (Wim van Ackooij, Mathematical Reviews, November, 2019)
- Table of contents (9 chapters)
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A Convex Optimization Toolbox
Pages 1-74
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Semidefinite and Semi-infinite Programming
Pages 75-116
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An Integration Toolbox
Pages 117-164
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Risk Measures
Pages 165-176
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Sampling and Optimizing
Pages 177-200
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Table of contents (9 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Convex and Stochastic Optimization
- Authors
-
- J. Frédéric Bonnans
- Series Title
- Universitext
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-14977-2
- DOI
- 10.1007/978-3-030-14977-2
- Softcover ISBN
- 978-3-030-14976-5
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- XIII, 311
- Topics
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