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Engineering  |  Dimitri Bertsekas

Abstract Dynamic Programming, 2nd Edition, 2018

by Dimitri P. Bertsekas

 

 

The 2nd edition of the research monograph “Abstract Dynamic Programming,” has now appeared and is available in hardcover from the publishing company, Athena Scientific, or from Amazon.com.

The 2nd edition aims primarily to amplify the presentation of the semicontractive models of Chapter 3 and Chapter 4 of the first (2013) edition, and to supplement it with a broad spectrum of research results that I obtained and published in journals and reports since the first edition was written (see below). As a result, the size of this material more than doubled, and the size of the book increased by nearly 40%.

 

 

Contents and Preface, 2ND EDITION

Chapter 1, 2ND EDITION, Introduction

Chapter 2, 2ND EDITION, Contractive Models

Chapter 3, 2ND EDITION, Semicontractive Models

Chapter 4, 2ND EDITION, Noncontractive Models

Appendixes and References, 2ND EDITION

In addition to the changes in Chapters 3, and 4, I have also eliminated from the second edition the material of the first edition that deals with restricted policies and Borel space models (Chapter 5 and Appendix C). These models are motivated in part by the complex measurability questions that arise in mathematically rigorous theories of stochastic optimal control involving continuous probability spaces. The restricted policies framework aims primarily to extend abstract DP ideas to Borel space models. Since this material is fully covered in Chapter 6 of the 1978 monograph by Bertsekas and Shreve, and followup research on the subject has been limited, I decided to omit Chapter 5 and Appendix C of the first edition from the second edition and just post them below.

Chapter 5 of 1st Edition

Appendix C of 1st Edition

 

Related Videos and Slides:

Video from a Oct. 2017 Lecture at UConn on Optimal control, abstract, and semicontractive dynamic programmingRelated paper, and set of Lecture Slides.

Video from a May 2017 Lecture at MIT on the solutions of Bellman’s equation, Stable optimal control, and semicontractive dynamic programmingRelated paper, and set of Lecture Slides.

Five-videolectures on Semicontractive Dynamic Programming.

 

Related Papers and Reports:

The following papers and reports have a strong connection to the book, and amplify on the analysis and the range of applications of the semicontractive models of Chapters 3 and 4: