Convex and Stochastic Optimization

J. Frédéric Bonnans (Autor)

Buch | Softcover

XIII, 311 Seiten

2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-14976-5 (ISBN)

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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.

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.

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.

"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)

“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)

Erscheinungsdatum	01.05.2019
Reihe/Serie	Universitext
Zusatzinfo	XIII, 311 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	504 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Convex Analysis • dynamic optimization • Lagrangian duality • Markov Decision Processes • Numerical Algorithms • optimal transport • Probability Theory • risk measures • Sample average approximation • semi-definite programming • Stochastic Programming
ISBN-10	3-030-14976-5 / 3030149765
ISBN-13	978-3-030-14976-5 / 9783030149765
Zustand	Neuware