Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. 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 nlodels (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 conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty 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 suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration.

Contains research articles on the mathematics and applications of control theory and on those parts of optimization theory concerned with the dynamics of deterministic or stochastic systems in continuous or discrete time or otherwise dealing with differential equations, dynamics, infinite-dimensional spaces, or fundamental issues in variational analysis and geometry.

Seeks to improve communication between managers and professionals in OR/MS.

This book contains a selection of papers presented at the conference on High Performance Software for Nonlinear Optimization (HPSNO97) which was held in Ischia, Italy, in June, 1997. The book provides an overview of the nonlinear optimization field, including algorithms, software evaluation, implementation issues, applications, and areas of research, through authoritative papers by some of the most active and well-known researchers in the field. The papers of the Proceedings can be recommended to mathematicians, physicists, and engineers working in the fields mentioned above, as well as recommended for further reading within graduate studies.