Techniques of Variational Analysis - (CMS Books in Mathematics) by Jonathan Borwein & Qiji Zhu (Hardcover)

Book Synopsis

Variational arguments are classical techniques whose use can be traced back to the early development of the calculus of variations and further. Rooted in the physical principle of least action they have wide applications in diverse fields. This book provides a concise account of the essential tools of infinite-dimensional first-order variational analysis. These tools are illustrated by applications in many different parts of analysis, optimization and approximation, dynamical systems, mathematical economics and elsewhere. Much of the material in the book grows out of talks and short lecture series given by the authors in the past several years. Thus, chapters in this book can easily be arranged to form material for a graduate level topics course. A sizeable collection of suitable exercises is provided for this purpose. In addition, this book is also a useful reference for researchers who use variational techniques---or just think they might like to.

From the Back Cover

Variational arguments are classical techniques whose use can be traced back to the early development of the calculus of variations and further. Rooted in the physical principle of least action they have wide applications in diverse fields. This book provides a concise account of the essential tools of infinite-dimensional first-order variational analysis illustrated by applications in many areas of analysis, optimization and approximation, dynamical systems, mathematical economics and elsewhere. The book is aimed at both graduate students in the field of variational analysis and researchers who use variational techniques, or think they might like to. Large numbers of (guided) exercises are provided that either give useful generalizations of the main text or illustrate significant relationships with other results.

Jonathan M. Borwein, FRSC is Canada Research Chair in Collaborative Technology at Dalhousie University. He received his Doctorate from Oxford in 1974 and has been on faculty at Waterloo, Carnegie Mellon and Simon Fraser Universities. He has published extensively in optimization, analysis and computational mathematics and has received various prizes both for research and for exposition.

Qiji J. Zhu is a Professor in the Department of Mathematics at Western Michigan University. He received his doctorate at Northeastern University in 1992. He has been a Research Associate at University of Montreal, Simon Fraser University and University of Victoria, Canada.

Review Quotes

From the reviews:

"This book maps the progress that has been made since the publication of the Ekeland variational principle in 1974 in the development and application of the variational approach in nonlinear analysis. The authors are well equipped for their task. ... This monograph is distinctive for bringing out the unifying role of variational principles across nonlinear analysis, the numerous examples of their application, and for the insights communicated by the authors, drawing on their experience as key participants in their development." (Richard B. Vinter, Mathematical Reviews, Issue 2006 h)

"The book presents a nice treatment of known variational principles and their application in many fields of mathematics. ... Many exercises are provided at the end of all sections where the reader can reflect the main text and can get further generalizations of the results." (Jörg Thierfelder, Zentralblatt MATH, Vol. 1076, 2006)

"The aim of the book is to emphasize the strength of the variational techniques in various domains ... . The book contains a lot of exercises completing the main text ... . the book is directed to graduate students in the field of variational analysis. ... Researchers who use variational techniques or intend to do so, will find the book very useful too." (S. Cobzas, Studia Universitatis Babes-Bolyai Mathematica, Vol. LI (2), June, 2006)

About the Author

Jonathan M. Borwein, FRSC is Canada Research Chair in Collaborative Technology at Dalhousie University. He received his Doctorate from Oxford in 1974 and has been on faculty at Waterloo, Carnegie Mellon and Simon Fraser Universities. He has published extensively in optimization, analysis and computational mathematics and has received various prizes both for research and for exposition.

Qiji J. Zhu is a Professor in the Department of Mathematics at Western Michigan University. He received his doctorate at Northeastern University in 1992. He has been a Research Associate at University of Montreal, Simon Fraser University and

University of Victoria, Canada.