The finite-dimensional nonlinear complementarity problem (NCP) is a system
of finitely many nonlinear inequalities in finitely many nonnegative
variables along with a special equation that expresses the complementary
relationship between the variables and corresponding inequalities. This
complementarity condition is the key feature distinguishing the NCP from
a general inequality system, lies at the heart of all constrained optimization
problems in finite dimensions, provides a powerful framework for the
modeling of equilibria of many kinds, and exhibits a natural link between
smooth and nonsmooth mathematics. The finite-dimensional variational
inequality (VI), which is a generalization of the NCP, provides a broad
unifying setting for the study of optimization and equilibrium problems
and serves as the main computational framework for the practical solution
of a host of continuum problems in the mathematical sciences.

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Divided into two volumes, the book contains twelve main chapters, followed
by an extensive bibliography, a summary of main results and key
algorithms, and a subject index. The first volume consists of the first six
chapters, which present the basic theory of VIs and CPs. The second volume
consists of the remaining six chapters, which present algorithms of
various kinds for solving VIs and CPs. Besides the main text, each chapter
contains (a) an extensive set of exercises, many of which are drawn from
published papers that supplement the materials in the text, 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 bibliography contains more than 1,300
publications in the literature up to June 2002. This bibliography serves
two purposes: one purpose is to give the source of the results in the chapters,
wherever applicable; the other purpose is to give a documentation of
papers written on the VI/CP and related topics.