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Convex and Stochastic Optimization

  • Textbook
  • © 2019

Overview

Authors:
  1. J. Frédéric Bonnans

    1. Inria and CMAP, Ecole Polytechnique, Palaiseau, France

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  • 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

Part of the book series: Universitext (UTX)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiii
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  2. A Convex Optimization Toolbox

    • J. Frédéric Bonnans
    Pages 1-74

  3. Semidefinite and Semi-infinite Programming

    • J. Frédéric Bonnans
    Pages 75-116

  4. An Integration Toolbox

    • J. Frédéric Bonnans
    Pages 117-164

  5. Risk Measures

    • J. Frédéric Bonnans
    Pages 165-176

  6. Sampling and Optimizing

    • J. Frédéric Bonnans
    Pages 177-200

  7. Dynamic Stochastic Optimization

    • J. Frédéric Bonnans
    Pages 201-222

  8. Markov Decision Processes

    • J. Frédéric Bonnans
    Pages 223-266

  9. Algorithms

    • J. Frédéric Bonnans
    Pages 267-281

  10. Generalized Convexity and Transportation Theory

    • J. Frédéric Bonnans
    Pages 283-301

  11. Back Matter

    Pages 303-311
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Keywords

About this book

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.

Reviews

“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)

Authors and Affiliations

  • Inria and CMAP, Ecole Polytechnique, Palaiseau, France

    J. Frédéric Bonnans

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.

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