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Stochastic Multi-Stage Optimization

At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming

  • Book
  • © 2015

Overview

Authors:
  1. Pierre Carpentier

    1. ENSTA ParisTech, Palaiseau, France

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  2. Jean-Philippe Chancelier

    1. Mathématiques et Calcul Scientifique (CERMICS), École Nationale des Ponts et Chaussées ParisTech, Marne la Vallée, France

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  3. Guy Cohen

    1. CERMICS, École Nationale des Ponts et Chaussées ParisTech, Marne la Vallée, France

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  4. Michel De Lara

    1. École Nationale des Ponts et Chaussées ParisTech, Marne la Vallée, France

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  • Discusses the role of information in dynamic stochastic optimization problems
  • Proposes a typology of information structures to delineate those which are numerically tractable
  • Proposes discretization methods jointly handling the stochastic components and the information structure of tractable problems and studies convergence issues for numerically tractable information structures
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Preliminaries

    1. Front Matter

      Pages 1-1
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    2. Issues and Problems in Decision Making Under Uncertainty

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 3-26

    3. Open-Loop Control: The Stochastic Gradient Method

      • 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
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    2. Tools for Information Handling

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 65-93

    3. Information and Stochastic Optimization Problems

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 95-132

    4. Optimality Conditions for Stochastic Optimal Control (SOC) Problems

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 133-152

  4. Discretization and Numerical Methods

    1. Front Matter

      Pages 153-153
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    2. Discretization Methodology for Problems with Static Information Structure (SIS)

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 155-180

    3. Numerical Algorithms

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 181-207

  5. Convergence Analysis

    1. Front Matter

      Pages 209-209
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    2. Convergence Issues in Stochastic Optimization

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 211-252

  6. Multi-Agent Systems

    1. Front Matter

      Pages 253-253
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    2. Multi-Agent Decision Problems

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 255-292

    3. Dual Effect for Multi-Agent Stochastic Input-Output Systems

      • Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara
      Pages 293-307

  7. Back Matter

    Pages 309-362
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Keywords

About this book

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.

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)

Authors and Affiliations

  • ENSTA ParisTech, Palaiseau, France

    Pierre Carpentier

  • Mathématiques et Calcul Scientifique (CERMICS), École Nationale des Ponts et Chaussées ParisTech, Marne la Vallée, France

    Jean-Philippe Chancelier

  • CERMICS, École Nationale des Ponts et Chaussées ParisTech, Marne la Vallée, France

    Guy Cohen

  • École Nationale des Ponts et Chaussées ParisTech, Marne la Vallée, France

    Michel De Lara

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

  • DOI: https://doi.org/10.1007/978-3-319-18138-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing Switzerland 2015

  • Hardcover ISBN: 978-3-319-18137-0Published: 19 May 2015

  • Softcover ISBN: 978-3-319-36515-2Published: 09 October 2016

  • eBook ISBN: 978-3-319-18138-7Published: 05 May 2015

  • 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

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