Customer Reviews

Dynamic Programming and Optimal Control, Vol. 1 (Optimization and Computation Series)

5 star:		(1)
4 star:		(0)
3 star:		(2)
2 star:		(0)
1 star:		(0)

 

 

This book does a very good job presenting both deterministic and stochastic optimal control. The author does a particularly good job in presenting the derivation of the Bellman equation and its relation to variational formulations for deterministic optimal control. There are also many very good problems with which the reader can test her understanding, and the author has made many solutions available on his web page. Problems range from testing theoretical understanding to determinig optimal policies for various control problems. There are even some exercises which ask the reader to develop parallel codes to solve some problems, so I think there is something in this book for everybody. Richard Bellman once said that there is considerably more to optimal control than just locating the eigenvalues of some matrix in the complex plane. I believe that Bertsekas has remained faithful to Bellman's view with the broad range of problems which he attacks through dynamic programming. I am currently doing a PhD thesis in mathematics studying Bellman equations, and I cannot think of a better source for intuition about control problems than Bertsekas' book. He even does a nice job in pointing out where he has omitted technicalities in the mathematical treatment for those who wish a very rigorous approach to control. If there is a better book out there, I am not aware of it.

After having been exposed to (and purchased) a number of books by Dr. Bertsekas on an eclectic array of topics, I have little doubt about his superb acumen and mastery of many, many subject areas involving applied mathematics. This book is no exception. Further, the legibility of Bertsekas' books score much higher the other two members of the GMTM (the Greek Math Triad of MIT), namely Bertsimas and Tsitsiklis, whose writings are highly esoteric in the purest form of the Archimedian tradition.

However, despite applaudable efforts to make the book more accessible to those on a lower IQ scale than the top-shelf MIT doctoral students, Bertsekas' 2-volume set on DP & Optimal Control still falls short in two key areas: (1) Visualization; and (2) Inconsistency in flow.

Being a product of the multi-media era, I and many of my fellow students are highly-dependent on visualization tools. In my opinion, what is NOT conveyed through lines and lines of cryptic (and author-specific) symbolism and mathematical formulation CAN be effectively conveyed through the strategic (and reasonably-ample) use of graphs and diagrams. Once the reader has a general idea of the gist of the concepts, then the specifics can be stated using precise mathematical language. But until then, the formulations are subject to open and erroneous interpretation (much the same way that few students are able to decipher the true essence of Symphony No. 40 by merely staring at the musical notes on sheets of paper). A picture is worth a thousand Greek symbols.

Inconsistency in flow refers to the fact that certain basic concepts are overstated in the book, while some of the more critical concepts (particularly those involving not-so-obvious algebraic steps in the proofs) are deemed "trivial" by the author, and apparently skipped for the sake of keeping the book to a manageable size. My suggestion is to err on the side of over-inclusion by keeping the proofs to a minimal in the actual text, but making the proofs (with all "trivial" elaborations) available online through the publisher's website (or via an included CD-ROM).

The aforesaid aside, the book is one of the best efforts in providing a comprehensive and modern analysis of DP/MDP, and its later editions do have the potential to claim 4.5-5 stars. In the interim, I recommend Powell's Approximate DP book as a less painful way of learning what I personally consider to be one of the most important topics in combinatorial optimization.

This book has so many unnecessary material in it. This makes you tired if you want to read it as your course book. I think Bertsekas, is more busy to write as many as book he can instead of making them readable.