Finite-Dimensional Variational Inequalities and Complementarity Problems (Springer Series in Operations Research and Financial Engineering) 2003rd Edition by Francisco Facchinei (PDF)

Description

This is part one of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It covers the basic theory of finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.

User’s Reviews

Editorial Reviews: Review From the reviews:”The first volume consists of the first six chapters, which present the basic theory of VIs and CPs. … Besides the main text, each chapter contains (a) an extensive set of exercises … and (b) a set of notes and comments that document historical accounts, give the sources for the results in the main text, and provide discussions and references on related topics and extensions. … The book is written very well and is an important contribution to the fields of VIs and CPs.” (Jürgen Guddat, Zentralblatt MATH, Vol. 1062 (13), 2005)”This … monograph presents a comprehensive and state-of-the-art treatment of variational inequalities (VI) in finite dimensions. … The presentation is clear, consistent, and essentially self-contained. The book contains a lot of new research material and recent results … . The discussion of related literature is a mine both for researchers and new comers … . the book is of high value not only for specialists, but for a wide range of readers … . It may recommended both for researchers and advanced students … .” (Diethard Klatte, OR-News, March, 2005)”Represents a successful endeavour resulting in a valuable source for researchers, advanced graduates, and for practitioners with an applied mathematics background. It will also well augment a library’s section on variational inequalities (VIs) and complementarity problems (CPs). … merits of the book include the motivation and guideline at the beginning of each chapter, a variety of exercises, further discussion in the form of notes and comments and pointers to the relevant literature at the end of each chapter, and a comprehensive reference list … .” (M Hintermueller, Journal of the Operational Research Society, Vol. 55 (9), 2004)”This … monograph, written for novice and expert researchers and advanced graduate students in a wide range of disciplines, presents a comprehensive, state-of-the-art treatment of the finite-dimensional variational inequality and complementarity problem … . It includes every major aspect of VI/CP … including novel application domains.” (Quarterly of Applied Mathematics, Vol. LXI (3), 2003)

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

⭐I bought both volumes (from a different site, at a lower price) — they have been absolutely indispensable. I heartily recommend them to anyone with a serious interest in the field (and I’ve been working with related techniques for several decades).Facchinei and Pang are both world-class researchers in this field. Their presentation is quite thorough, yet the overall points are easy to grasp. Knowing how to pose problems is nice, but without solution algorithms, it is useless. Thus, it is very helpful that vol 2 includes many different kinds of algorithms, as well as detailed discussions of their properties.Both volumes definitely require “mathematical maturity.” However, mathematical maturity is essential for this material — whether you intend to implement working algorithms or to appreciate the beauty of these problems and algorithms. The first volume is heavy on theory, while the second concentrates on solution algorithms; I’d definitely get the first if you are interested in the second.The only drawback is that they do not include small problems and solutions.Aside: the 1-star ratings of Volume 1 are astonishing. Comparing the books to the reviews, it’s hard to believe they read the book.

⭐I am very familiar with this scholarly book, by far the most useful and comprehensive on the important (although somewhat specialized) subject of variational inequalities. I have found it useful on several occasions, as have many other researchers. I am writing this review because I find unfair and appalling the two nonfactual and anti-intellectual customer reviews from 2004.One customer, without citing examples, says that “a sampling revealed that a lot of it is false”. I am a reasonable expert in the field and have not found anything false so far. Indeed the book is written with great care and high standards of mathematical rigor.The other customer dismisses the book by saying “if you believe this, I have a bridge to sell you”. I actually believe almost all he has written, indeed I find it a fairly accurate description of the book!

⭐I borrowed this book(both volumns) from U of Chicago Library and read it carefully. It provides very good information on variational inequalities of different kinds. It’s easy to read and follow. I like it so much and that’s why I search this book in amazon to buy one for myself.

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