This is part one of a two-volume work presenting a definitive and comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. This volume covers the basic theory needed and should appeal to mathematicians, economists, and engineers working in the area.

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 thefinite-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)

Klappentext

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.

Inhalt
Solution Analysis I.- Solution Analysis II.- The Euclidean Projector and Piecewise Functions.- Sensitivity and Stability.- Theory of Error Bounds.