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Rating: 
Summary: Proximal point algorithms by Censor and Zenios
Review: Part I of this book starts with an aphorism,
attributed to H. von Helmholtz:
``The most practical thing in the world
is a good theory.''
The book does justice to von Helmholtz maxim.
The theory of Bregman distances is presented
in a clear, geometrical and intuitive way.
Part II of the book presents several important
and illustrative applications of Proximal Point
algorithms, to constrained optimization,
Maximum Entropy problems, financial stochastic
networks, and several other important areas.
Rating:
Summary: Proximal point algorithms by Censor and Zenios
Review: Part I of this book starts with an aphorism,
attributed to H. von Helmholtz:
``The most practical thing in the world
is a good theory.''
The book does justice to von Helmholtz maxim.
The theory of Bregman distances is presented
in a clear, geometrical and intuitive way.
Part II of the book presents several important
and illustrative applications of Proximal Point
algorithms, to constrained optimization,
Maximum Entropy problems, financial stochastic
networks, and several other important areas.
Rating: 
Summary: For the dedicated specialist
Review: This book is highly mathematical. It phrases its points as a series of theorems, with a number of case studies at the end. The theorems all stop just short legible technique. The examples, though exciting, all presuppose command of technique. I regret that I never found that missing piece within myself. That piece was the one that connects deep theorems about abstract N-dimensional pseudodistances into working fluency about CAT scans. I did, however, get some understanding of the kinds of problems that the authors address. They are some of the analytic functions, with linear or nonlinear constraints. In particular, they are functions of high dimensions - thousands or millions of constraints - amenable to fairly fine-grained optimization. They are not discrete problems, like the Travelling Salesman. They are not problems with hugely jagged reward surfaces, like "motif finding" problems in bioinformatics. They are not genetic algorithms, Monte Carlo searches, or combinatorial problems. The authors do in fact parallelize a number of important optimization problems, including CAT scans, transportation planning, and radiation therapy, but not all optimization techniques. Those problems span only a small part of the parallelizable world. The broad promise in the title "Parallel Optimization" was only partly kept. Some parallelization techniques were presented, as well as some interesting perspetives on numerical optimization. Optimization is a large field, however, and this is only a small map. Still, for that range of problems, it seems to offer the right reader profound insight. I can not be sure, though, since I'm not the right reader. I give it three stars, just because I had to give something. Different people will assign this book very different value.
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