Nonlinear Optimizationby Andrzej Ruszczynski, Andrzej Ruszczynski
Pub. Date: 01/02/2006
Publisher: Princeton University Press
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers/i>
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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.