Quadratic Programming and Affine Variational Inequalities / Nonconvex Optimization and Its Applications Bd.78 (PDF)
This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequalities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an...
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This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational 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 briefly discuss two concrete models (a linear fractional vector optimization and a traffic equilibrium problem) whose analysis can benefit greatly from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of continuity and differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequalities where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequalities under linear perturbations are studied in three other chapters.
One special feature of this 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 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.
Audience
This book is intended for graduate and postgraduate students in applied mathematics, as well as researchers in the fields of nonlinear programming and equilibrium problems. It can be used for some advanced courses on nonconvex quadratic programming and affine variational inequalities.
- Autoren: Gue Myung Lee , N. N. Tam , Nguyen Dong Yen
- 2006, 2005, 346 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 0387242783
- ISBN-13: 9780387242781
- Erscheinungsdatum: 30.03.2006
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- Dateiformat: PDF
- Grösse: 14 MB
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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 Gómez Bofill, Zentralblatt MATH, Vol. 1092 (18), 2006)
"This book presents a theory of qualitative aspects of nonconvex quadratic programs and affine variational inequalities. … 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. … Most of the proofs are presented in a detailed and elementary way. … Whenever possible, the authors give examples illustrating their results. … In summary, this book can be recommended for advanced students in applied mathematics due to the clear and elementary style of presentation. … 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)
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