Stochastic Multi-Stage Optimization

At the Crossroads between Discrete Time Stochastic Control and Stochastic Programming

Pierre Carpentier, Jean-Philippe Chancelier, Guy Cohen, Michel De Lara (Autoren)

Buch | Hardcover

XVII, 362 Seiten

2015 | 2015
Springer International Publishing (Verlag)
978-3-319-18137-0 (ISBN)

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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.

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.

I Preliminaries.- 1.Issues and Problems in Decision Making under Uncertainty.- 2.Open-Loop Control: The Stochastic Gradient Method.- II Decision under Uncertainty and the Role of Information.- 3.Tools for Information Handling.- 4.Information and Stochastic Optimization Problems.- Optimality Conditions for SOC Problems.- III Discretization and Numerical Methods.- 6.Discretization Methodology for Problems with SIS.- 7.Numerical Algorithms.- IV Convergence Analysis.- 8.Convergence Issues in Stochastic Optimization.- V Advanced Topics.- 9.Multi-Agent Decision Problems.- Dual Effect for Multi-Agent Stochastic I-O Systems.- VI Appendices.- A. Basics in Analysis and Optimization.- B. Basics in Probability.- References.- Index.

"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)

Erscheint lt. Verlag	19.5.2015
Reihe/Serie	Probability Theory and Stochastic Modelling
Zusatzinfo	XVII, 362 p. 45 illus., 14 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	707 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	93C15, 93C39, 49-XX, 60-XX • discretization • dynamical information • numerical approximation • Optimization • Stochastic Optimal Control • Stochastic Programming
ISBN-10	3-319-18137-8 / 3319181378
ISBN-13	978-3-319-18137-0 / 9783319181370
Zustand	Neuware