The research monograph "Abstract Dynamic Programming," published in 2013, may be ordered in hardcover from the publishing company, Athena Scientific, or from Amazon.com.
The research monograph provides a synthesis of research on the foundations of dynamic programming that started nearly 50 years ago, with the modern theory of approximate dynamic programming and the new class of semicontractive models.
It aims at a unified and economical development of the core theory and algorithms of total cost sequential decision problems, based on the strong connections of the subject with fixed point theory. The analysis focuses on the abstract mapping that underlies dynamic programming and defines the mathematical character of the associated problem. The discussion centers on two fundamental properties that this mapping may have: monotonicity and (weighted sup-norm) contraction. It turns out that the nature of the analytical and algorithmic DP theory is determined primarily by the presence or absence of these two properties, and the rest of the problem's structure is largely inconsequential. New research is focused on two areas:
Click here to visit the book's web site at Athena Scientific for contents, preface, Chapter 1, slides, videos, and other instructional material, or to order the book directly from the publisher for faster service.
The following documents 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:
A second edition of the book, incorporating much of the research in the preceding documents, is currently in preparation.
The second edition will be essentially identical to the first edition, except for Chapter 3 and Sections 4.4-4.7, which will be substantially revised.
Drafts of the two modified chapters are posted here: Chapter 3 and Chapter 4. They will be updated periodically up to the publication of the second edition, and they will remain on line after publication for the benefit of readers of the first edition.