Quadratic Programming and Affine Variational Inequalities: A Qualitative Study (Nonconvex Optimization and Its Applications) (Hardcover)by Gue M. Lee (Author), Nguyen N. Tam (Author), Nguyen D. Yen (Author)

Key Phrases: local solution set, lsc property, polyhedral convex set, Frank-Wolfe Theorem, Eaves Theorem, Farkas Lemma


Review
From the reviews: "This book presents a detailed exposition of qualitative results for quadratic programming (QP) and affine variational inequalities (AVI). Both topics are developed into a unifying approach." (Walter GA3mez Bofill, Zentralblatt MATH, Vol. 1092 (18), 2006) "This book presents a theory of qualitative aspects of nonconvex quadratic programs and affine variational inequalities. a ] Applications to fractional vector optimization problems and traffic equilibrium problems are discussed, too. The book is a valuable collection of many basic ideas and results for these classes of problems, and it may be recommended to researchers and advanced students not only in the field of optimization, but also in other fields of applied mathematics." (D. Klatte, Mathematical Reviews, Issue 2006 e) "This book presents a qualitative study of nonconvex quadratic programs and affine variational inequalities. a ] Most of the proofs are presented in a detailed and elementary way. a ] Whenever possible, the authors give examples illustrating their results. a ] In summary, this book can be recommended for advanced students in applied mathematics due to the clear and elementary style of presentation. a ] this book can be serve as an interesting reference for researchers in the field of quadratic programming, finite dimensional variational inequalities and complementarity problems." (M. Stingl, Mathemataical Methods of Operations Research, Vol. 65, 2007)

Product Description
This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequalities. One special feature of the book is that when a certain property of a characteristic map or function is investigated, the authors always try first to establish necessary conditions for it to hold, then they go on to study whether the obtained necessary conditions are also 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.