Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the theories
of mathematical programming and variational inequalities, respec-
respectively. This book develops a unified theory on qualitative aspects of
nonconvex quadratic programming and affine variational inequal-
inequalities. The first seven chapters introduce the reader step-by-step
to the central issues concerning a quadratic program or an affine
variational inequality, such as the solution existence, necessary and
sufficient conditions for a point to belong to the solution set, and
properties of the solution set. The subsequent two chapters discuss
briefly two concrete models (linear fractional vector optimization
and the traffic equilibrium problem) whose analysis can benefit a lot
from using the results on quadratic programs and affine variational
inequalities. There are six chapters devoted to the study of continu-
continuity and/or differentiability properties of the characteristic maps and
functions in quadratic programs and in affine variational inequali-
inequalities where all the components of the problem data are subject to
perturbation. Quadratic programs and affine variational inequali-
inequalities under linear perturbations are studied in three other chapters.
One special feature of the presentation is that when a certain prop-
property of a characteristic map or function is investigated, we always
try first to establish necessary conditions for it to hold, then we
go on to study whether the obtained necessary conditions are suffi-
sufficient ones. This helps to clarify the structures of the two classes of
problems under consideration. The qualitative results can be used
for dealing with algorithms and applications related to quadratic
programming problems and affine variational inequalities.