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© 2015

Stochastic Multi-Stage Optimization

At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming

Book

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 75)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 3-26
    3. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 27-62
  3. Decision Under Uncertainty and the Role of Information

    1. Front Matter
      Pages 63-63
    2. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 65-93
    3. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 95-132
    4. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 133-152
  4. Discretization and Numerical Methods

    1. Front Matter
      Pages 153-153
    2. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 155-180
    3. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 181-207
  5. Convergence Analysis

    1. Front Matter
      Pages 209-209
    2. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 211-252
  6. Multi-Agent Systems

    1. Front Matter
      Pages 253-253
    2. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 255-292
    3. Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 293-307
  7. Back Matter
    Pages 309-362

About this book

Introduction

The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.

Keywords

93C15, 93C39, 49-XX, 60-XX discretization dynamical information numerical approximation optimization stochastic optimal control stochastic programming

Authors and affiliations

  1. 1.ENSTA ParisTechPalaiseauFrance
  2. 2.Mathématiques et Calcul Scientifique (CERMICS)École Nationale des Ponts et Chaussées ParisTechMarne la ValléeFrance
  3. 3.CERMICSÉcole Nationale des Ponts et Chaussées ParisTechMarne la ValléeFrance
  4. 4.École Nationale des Ponts et Chaussées ParisTechMarne la ValléeFrance

About the authors

Professor Pierre Carpentier’s primary research areas are Decomposition and Coordination for the Optimization of Large-Scale Systems in the stochastic framework, with a special interest in numerical methods. He is currently working at the applied mathematics unit UMA, ENSTA ParisTech, France. Professor J. Ph. Chancelier’s research contributions have been in the fields of Stochastic Optimization, Control and Computer Languages for Numerical Computations. He currently holds a position at the applied mathematics center research CERMICS, École des Ponts ParisTech, France. The main research contributions of Professor Guy Cohen have been in the theory of Decomposition and Coordination for the Optimization of Large-Scale Systems, in the development of a “linear” theory of a certain class of Discrete Event Systems based on the use of the so-called Max-Plus algebra, and more recently in numerical methods for Stochastic Optimal Control. He is currently a Researcher Emeritus. Professor Michel De Lara’s main theoretical research fields are control theory and stochastic control. With regard to applications, he specializes in developing mathematical methods for the sustainable management of natural resources, concentrating on renewable energy and biodiversity. He currently holds a position at the applied mathematics center research CERMICS, École des Ponts ParisTech, France.

Bibliographic information

  • Book Title Stochastic Multi-Stage Optimization
  • Book Subtitle At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming
  • Authors Pierre Carpentier
    Jean-Philippe Chancelier
    Guy Cohen
    Michel De Lara
  • Series Title Probability Theory and Stochastic Modelling
  • Series Abbreviated Title Probability and Stochastic (formerly: PIA & SMAP)
  • DOI https://doi.org/10.1007/978-3-319-18138-7
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-18137-0
  • Softcover ISBN 978-3-319-36515-2
  • eBook ISBN 978-3-319-18138-7
  • Series ISSN 2199-3130
  • Series E-ISSN 2199-3149
  • Edition Number 1
  • Number of Pages XVII, 362
  • Number of Illustrations 31 b/w illustrations, 14 illustrations in colour
  • Topics Continuous Optimization
    Probability Theory and Stochastic Processes
  • Buy this book on publisher's site

Reviews

“I consider the book as a guide to the different aspects of stochastic optimization and the most important motive for distinguishing it from other similar textbooks and monographs is a great emphasis put on the role of information.” (Jerzy Ombach, zbMATH 1336.90066, 2016)