Convex Optimization & Euclidean Distance Geometry by Jon Dattorro (PDF)

Description

Convex Analysis is the calculus of inequalities while Convex Optimization is its application. Analysis is inherently the domain of the mathematician while Optimization belongs to the engineer. In layman’s terms, the mathematical science of Optimization is the study of how to make a good choice when confronted with conflicting requirements. The qualifier Convex means: when an optimal solution is found, then it is guaranteed to be a best solution; there is no better choice. As any Convex Optimization problem has geometric interpretation, this book is about convex geometry (with particular attention to distance geometry), and nonconvex, combinatorial, and geometrical problems that can be relaxed or transformed into convex problems. A virtual flood of new applications follows by epiphany that many problems, presumed nonconvex, can be so transformed. Revised & Enlarged International Paperback Edition III

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I thought I’d use this book as a reference since the unusually large Index is a good place to locate the definitions. Dattorro starts from the basic premises and works through the algebra with many examples and many good illustrations.I’ve found that Dattorro’s perspective on each subject (optimization and distance geometry) is both algebraic and geometric. He bridges those unexpectedly well. His approach to rank minimization, for example, is how I would have thought of doing it, in terms of eigenvalues. It feels right to me.Dattorro’s notation is “progressive.” A vector is represented by a single letter, say x, with no embellishment to distingush it from a real variable. That makes the presentation simple, but takes some getting used to as does his style of “missing articles” (e.g. the) and replacement everywhere of “i.e.” with latin “id est.”The book is organized by convex optimzation first then distance geometry second,three chapters devoted to each. The appendices support seven chapters total and take half the book! It’s a big book.Dattorro’s treatment of distance geometry is the book’s main strength. The main result is a new expression for the relationship between the semidefinite positive and Euclidean distance cones, and takes a long time to get there. Along the way, he goes back to 1935 and integrates the results of Schoenberg (before modern linear algebra), Cayley and Menger, Critchley, Gower, then augments that with some later results like Hayden, Wells, Liu, & Tarazaga, and then more contemporary results like Deza & Laurent, Wolkowicz, Saul and Weinberger to name only a few. Then, of course he shows how that all relates to optimization. I particularly liked the geographical map reconstruction examples where only distance ordering was known.I recommend this book to anyone who wants both a good introduction to convex optimization and a reference to some latest techniques, a few of which Dattorro may have invented. There is a good review of semidefinite programming, and what he writes about distance geometry refreshes old math with new.

⭐I have read many books in optimization and in engineering, this is really one of the most exceptional books in my library. Dattorro is a talented writer. The book has plenty of illustrations that make the content of the book very easy to understand. The author is obviously influenced by Boyd

⭐and this is actually a very good thing. In my opinion he has extended Boyd’s book in the best possible way, by providing exciting applications and also a different perspective for understanding convexity, polytopes etc. The book is very useful for understanding Semidefinite {rogramming (SDP). To my knowledge this is the only book that gets so deeply in SDP (theory and mostly applications). The chapters on Euclidean Distance Geometry are unique in the sense that the only other books that I found in the literature on that topic date back to 1930. I think the biggest hit of the book is the algorithm for rank minimization.Unfortunately the book hasn’t gotten enough attention from the scientists and engineers probably because you can also get a free pdf copy for the author’s website. Although I can get a free online version, I bought a copy because it is worth it (as it is for Boyd’s book). I have recommended this book to may PhD students that got inspired for their research.

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