Customer Reviews

Nonlinear Optimization

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This outstanding book fills the need for a recent introductory graduate textbook in nonlinear convex optimization. The book is divided into 2 parts: Part I deals with theory while Part II deals with algorithms for nonlinear convex optimization. Topics covered in Part I include basic convex analysis, optimality conditions, and Lagrangian duality. There are a number of interesting examples distributed throughout the discussions in Part I - some of these examples include recent concepts like semidefinite programming. The author also highlights the importance of DIFFERENTIABILITY in convex optimization - in fact he devotes separate sections for the optimality conditions of smooth convex and nonsmooth convex problems. Part II discusses algorithms for smooth unconstrained and constrained optimization and finally subgradient, bundle, and trust region schemes for nondifferentiable optimization. The discussion on algorithms for nondifferentiable optimization is new and an important ingredient in this book - for more details one can refer to the 2 volume set by Hiriart-Urruty and Lemarechal. However, there is no discussion on INTERIOR POINT METHODS and this is the only notable omission in the book. For more on interior point methods in nonlinear optimization, one can refer to the recent book by Nocedal and Wright. Personally, I enjoyed this book immensely, and I look forward to using it in a graduate course on nonlinear optimization.

The most important feature of this book is the systematic, theory-driven presentation. Proofs of all statements are supported by instructive examples in statistics, finance, economics, and engineering. The analysis covers a broad array of problems, including nondifferentiable and nonconvex. The chapter on duality contains several interesting economic applications. Methods are presented in a transparent way, with convergence proofs and rate of convergence estimates. The chapter on methods for nondifferentiable optimization is quite valuable, because there are few sources with this material. Solutions to problems, some of which are tricky, would help, and I hope that they will be included in the next edition.

Easy to read, quite complete, with a lot of examples and exercises. There is a good part on theory (convex sets and functions, subdifferentiability), another big part on numerical differentiable optimization, and a good introduction on non-differentiable optimization.

I'm a recent Ph.D. graduate in Operations Research and during the last 4 years this book has been one of my main tools in both my studies and academic research. This book is a comprehensive introduction to nonlinear programming and is divided in two parts.; Part I covers the main theoretical considerations and Part II covers many important optimization methods. I would say that the main feature of this book is that it manages, in a clear and concise way, to take the reader from the very basics of optimization to advanced and current topics of nonlinear optimization. In particular, it covers the theory and methods of convex optimization of non-differentiable functions where the important concepts of subdifferentials and conjugate duality come into play. From my opinion, these are necessary tools for any aspiring researcher in optimization theory and I haven't seen yet a more understandable and concise presentation of these subjects. Another area where this book shines is in it's examples and applications. Contrary to many mathematical introductory books, I would say that every example of this book is non-trivial and of some theoretical or applied value. It is in these examples and applications where the reader can see the real value of the developed theory and methods. Believe me when I say that more than once you'll be referring back to the examples to get ideas for even your own research. All said, I really enjoyed this book and value highly it's contents.