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Nonlinear Optimization, by Andrzej Ruszczynski
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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 to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures.
The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems.
Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.
- Sales Rank: #1827981 in eBooks
- Published on: 2011-09-19
- Released on: 2011-09-19
- Format: Kindle eBook
Review
"This book offers a very good introduction to differentiable and nondifferentiable nonlinear optimization theory and methods. With no doubt the major strength of this book is the clear and intuitive structure and systematic style of presentation. This book can be recommended as a material for both self study and teaching purposes, but because of its rigorous style it works also as a valuable reference for research purposes."--Mathematical Modeling and Operational Research
"This is one of the best textbooks on nonlinear optimization I know. Focus is on both theory and algorithmic solution of convex as well as of differentiable programming problems."--Stephan Dempe, Zentralblatt MATH Database
"In summary, this book competes with the topmost league of books on optimization. The wide range of topics covered and the thorough theoretical treatment of algorithms make it not only a good prospective textbook, but even more a reference text (which I am happy to have on my shelf.)"--Franz Rendl, Operations Research Letters
"Throughout the book the writing style is very clear, compact and easy to follow, but at the same time mathematically rigorous. The proofs are easy to follow because the author usually carefully explains every move. In addition the meaning of the most central results is usually demonstrated with examples and in many cases explanations are also supported by visualizations...This book offers a very good introduction to differentiable and nondifferentiable nonlinear optimization theory and methods...Recommended as a material for both self study and teaching purposes"--Petri Eskelinen, Mathematical Methods of Operation Research
From the Back Cover
"Nonlinear Optimization will become the standard textbook on its subject, as well as a reference book that everyone will want to own. Not only is it beautiful and elegant, it is also utterly comprehensive and modern, with many realistic and interesting examples."--Robert J. Vanderbei, Princeton University, author of Linear Programming
"This excellent book is the best I have reviewed in the past ten years. Very well written, its three main strengths are its treatment of theory and algorithms on equal terms, its mathematically driven presentation of the material, and its interesting examples and applications."--Ekkehard W. Sachs, Virginia Tech and Universität Trier
About the Author
Andrzej Ruszczynski is Professor of Operations Research at Rutgers University. He is the coauthor of "Stochastic Programming" and the coeditor of "Decision Making under Uncertainty".
Most helpful customer reviews
11 of 11 people found the following review helpful.
Excellent introduction to theory and algorithms for nonlinear optimization
By Kartik Sivaramakrishnan
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.
8 of 9 people found the following review helpful.
An interesting and useful book
By Pat Tever
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.
2 of 2 people found the following review helpful.
An indispensable book on nonlinear optimization
By Ricardo A. Collado
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.
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