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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.
List of 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.
About the author
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.
Summary
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.
Report
"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)
