David Tranah, Cambridge University Press, Publishing Division
The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU. United Kingdom
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Author Questionnaire
1.1 Authors Jonathan Michael Borwein and Jon Dwight Vanderwerff
1.2 Book title Convex Functions:
Constructions, Characterizations and Counterexamples
1.3 Full names Jonathan Michael Borwein and Jon Dwight Vanderwerff
1.4 Name on title page Jonathan M. Borwein and Jon D. Vanderwerff
1.5 Nationality Jonathan M. Borwein (Canadian and UK)
Jon D. Vanderwerff (Canadian)
1.6 Your present affiliation
Jonathan M. Borwein Canada Research Chair, Dalhousie University, Halifax NS Canada B3H 1W5 and Laureate Professor University of Newcastle, NSW 2308 Australia
Jon D. Vanderwerff Professor of Mathematics, La Sierra University, Riverside, CA 92515, USA
1.7 Short autobiographical note
Jonathan M. Borwein was Shrum Professor of Science (1993-2003) and a Canada Research Chair in Information Technology (2001-08) at Simon Fraser University, and was founding Director of the Centre for Experimental and Constructive Mathematics. In 2004, he (re-)joined the Faculty of Computer Science at Dalhousie as a Canada Research Chair in Distributed and Collaborative Research. He was born in St Andrews in 1951, and received his D.Phil from Oxford in 1974, as a Rhodes Scholar. Prior to joining SFU in 1993, he worked at Dalhousie (1974-91), Carnegie-Mellon (1980-82) and Waterloo (1991-93). He is presently Visiting Professor Laureate at the University of Newcastle, NSW.
Awards and Honours He has received various awards including the Chauvenet Prize of the MAA (93), Fellowship in the Royal Society of Canada (94), Fellowship in the American Association for the Advancement of Science (02), an honorary degree from Limoges (99), and foreign membership in the Bulgarian Academy of Sciences (03).
Administration Dr. Borwein was Governor at large of the MAA (2004-07), is a past President of the Canadian Mathematical Society (2000-02) and past Chair of (the National Science Library) NRC-CISTI's Advisory Board (2001-2003). He was recently Chair of the Executive of C3.ca--the national HPC Consortium, a Member of the Atlantic Comput. Excellence Network Executive (www.ace-net.ca) and chaired the International Math Union's Committee on Electronic Information and Communications (www.ceic.math.ca, 2002-2008). During 2006 he was Director of the Atlantic Association for Research in the Mathematical Sciences (www.aarms.math.ca). He is a member at large of the Board of the Academy of Science of the Royal Society of Canada (2007-09) and the Selection Committee for the Canadian Science and Technology Hall of Fame (2006-08).
Research His interests span pure (analysis), applied (optimization), computational (numerical and computational analysis) mathematics, and high performance computing. He has authored a dozen books---most recently three on Experimental Mathematics (www.expmath.info) and a monograph on Techniques of Variational Analysis---and over 300 refereed articles.
Computing and Information Technology Dr Borwein is co-founder (1995) of a Halifax software company, MathResources (www.mathresources.com), producing highly interactive CD and Web software mainly for school and university mathematics. He is also a coauthor of Canada's Long Range Plan for advanced computing: Engines of Discovery (c3.ca, 2005 and 2007) and sits on the Canada-EC Information Science and Technology committee (2005-08). The ISI (http://isihighlycited.com/) has identified him as one of the 250 most cited mathematicians of the period 1980-1999.
Jon Vanderwerff is a professor of mathematics at La Sierra University. He held postdoctoral fellowships at University of Waterloo and Simon Fraser University after receiving his doctorate at the University of Alberta in 1992.
1.8 Dates of birth
Borwein May 20, 1951 Vanderwerff March 7, 1964
1.9 Professional associations/learned bodies.
Borwein: AMS, MAA, Australian Math Soc, Canadian Math Soc, Fellow AAAS, Fellow Royal Society of Canada, Foreign Member Bulgarian Academy of Science
Vanderwerff MAA
1.10 Addresses
Borwein School of Mathematical and Physical Sciences, University of Newcastle
Phone: Office 61-2-4921-5535 Home 61-2-4009-1468
e-mail:
web: www.cs.dal.ca/~jborwein
book url http://projects.cs.dal.ca/ddrive/ConvexFunctions/ has various related links and addenda (including any subsequent errata)
.
Vanderwerff Dept of Mathematics, La Sierra University, Riverside, CA 92515 USA
Phone: office: (951) 785-2553 home: (909) 799-6818 Fax: (951) 785-2164
e-mail:
web: http://faculty.lasierra.edu/~jvanderw
2.1 Your book: special features
· Treats convex functions in both Euclidean and Banach space
· Can be read at a variety of different levels and in extensor or for browsing
· Over 600 exercises: of theory and applications; at both routine and research level
· Extensive index and bibliography
· Much of the material has never appeared in book form; a significant amount is new within the book itself\
· Much of the material has already been taught or presented by the authors or their collaborators in various ways
2.2 Non-technical description
Convexity theory ... reaches out in all directions with useful vigor. Why is this so? Surely any answer must take account of the tremendous impetus the subject has received from outside of mathematics, from such diverse fields as economics, agriculture, military planning, and flows in networks. With the invention of high-speed computers, large-scale problems from these fields became at least potentially solvable. Whole new areas of mathematics (game theory, linear and nonlinear programming, control theory) aimed at solving these problems appeared almost overnight. And in each of them, convexity theory turned out to be at the core. The result has been a tremendous spurt in interest in convexity theory and a host of new results. (Roberts and Varberg, 1973)
Some say number theory is the Cauchy-Schwarz inequality. Just find what to `Cauchy with?’ Likewise, the right convex function resolves much mathematics. Topological, algebraic, and geometric notions then coincide and many different sources of insight are available. Also, while differentiability has been exploited throughout science since Newton, convexity, though it appears in derivative tests, linear programming, or inequality theory, barely enters the undergraduate corpus. This is a shame, especially since the recent “interior-point revolution” in linear programming has made convex computation easy while nonconvex remains hard---partly for the prosaic reason that local and global minima coincide in the convex case. Our book hopes to help redress this neglect.
2.3 Full description Our book on convex functions emerges out of fifteen years of collaboration between the authors. It is far from the first book on the subject nor will it be the last. It is neither a book on Convex Analysis such as Rockafellar's foundational 1970 book nor a book on Convex Programming such as Boyd and Vandenberghe's excellent recent CUP text There are a number of fine books---both recent and less so---on both those subjects or on Convexity and relatedly on Variational Analysis Such books complement or overlap in various ways with our own focus which is to explore the interplay between the structure of a normed space and the properties of convex functions which can exist thereon. In some ways, among the most similar books to ours are those of Phelps (Springer 1989) and of Giles (1982)} in that both also straddle the fields of geometric functional analysis and convex analysis---but unlike our book without the convex function itself being the central character.
We have structured this book so as to accommodate a variety of readers—both in level of sophistication and in background. This leads to some intentional repetition. Chapter one makes the case for the ubiquity of convexity, largely by way of example. Many but not all of which are detailed in later chapters. Chapter two then provides an extensive foundation for the study of convex functions in Euclidean (finite-dimensional) space, and Chapter Three reprises important special structures such as polyhedrality, selection theorems, eigenvalue optimization and semi-definite programming. Chapters four and five play the same role in (infinite-dimensional) Banach space. Chapter six discusses a number of other basic topics; such as selection theorems, set convergence, integral and trace class functionals, and convex functions on Banach lattices.
The remaining three chapters can be read largely independently of each other. Chapter seven examines the structure of Legendre functions which comprises those barrier functions which are essentially smooth and essentially strictly convex and considers how the existence of such barrier functions is related to the geometry of the underlying Banach space; as always the nicer the space (e.g., is it reflexive, Hilbert or Euclidean?) the more that can be achieved. This coupling between the space and the convex functions which may survive on it is attacked more methodically in Chapter eight.
Chapter nine investigates (maximal) monotone operators through the use of a recently discovered class of convex representative functions of which the Fitzpatrick function is the progenitor. We have written this chapter so as to make it better useable as a stand-alone source on convexity and its applications to monotone operators.
The first half of this chapter is based in large part on Borwein’s paper:
“Maximal Monotonicity via Convex Analysis," J. Convex Analysis, 13 (2006), 561--586 was identified in May 2008 as an ISI {Hot Paper in Math) http://sciencewatch.com/sciencewatch/dr/nhp/2008/08maynhp/08maynhpBorwein/
In each chapter we have included a variety of concrete examples and exercises---often guided, some with fuller notes given in Chapter nine. We both believe strongly that general understanding and intuition rely on having fully digested a good cross-section of particular cases.
3 Marketing Borwein is currently based in Australia
3.1 Buyers We think this book can be used as a text, either primary or secondary, for a variety of introductory graduate courses. One possible one-semester course would comprise Chapters one, two, three and the finite-dimensional parts of Chapters five through nine. These parts are listed at the end of Chapter three. Another course could encompass Chapters one through six along with Chapter nine, and so on.
We suspect that use as a primary text book will be limited. We believe that it will prove more valuable as a secondary source in graduate courses; and to a larger group of researchers and practitioners in mathematical science. In that spirit have tried to keep notation so that the infinite-dimensional and finite-dimensional discussion are well comported and so that the book can be dipped into as well as read sequentially. This also requires occasional intentional redundancy. In addition, we finish with a `bonus chapter' revisiting the boundary between Euclidean and Banach space and making additional comments on the material in the earlier chapters.
3.2 Countries Are there any countries or areas of the world in which there is particular interest in the subject dealt with by your book?
Yes, in Israel, France, Italy and Eastern Europe. Boyd and Vandenberghe’s book has also dramatically increased interest in the subject in electrical engineering. Likewise interior point methods have dramatically increased interest in Optimization/OR.
3.3 Competing books Please see 2.3
4.1 Catalogue mailing To which academic disciplines will the book be most relevant? Please list these in descending order of importance.
1. Mathematics
2. Optimization Operations Research
3. Electrical Engineering
4. Statistics
5. Physical Sciences
4.2 Newsgroups Some exist but we are not sure how useful a vehicle this would prove.
4.3 Societies Which professional societies, associations and/or industrial/commercial organisations will be most interested in your book?
· AMS, MAA, CMS, AustMS, AAAS (JMB belongs to these)
· SIAM, Math Programming, Infors, EMS, IEEE, ACM
4.4 Special Sales Probably not, although the Book club has made mass purchase of a couple of Borwein’s earlier books and various bulk sales (e.g., Smiths, UnwinHyman) of his Harper-Collin’s dictionary have been routine (it now has a Smithsonian imprint).
4.5 Individual buyers Reviewers for almost all smaller Math Societies with book review sections in their Notices or Bulletins.
4.6 Exhibitions The usual suspects and a various less frequent meetings in convex and nonlinear analysis and in Banach space theory: The Prague spring schools.
4.7 Prizes One can always aspire to a Steele prize! Borwein has won the Chauvenet Prize.
5.1 Publications J Convex Analysis (JMB an editor), J Convex and Nonlinear Analysis (JMB an editor), Set-valued and Variational Analysis (JMB an editor)
Almost all major Math Societies with book review sections in their Notices or Bulletins.
The American Scientist, Science News, Science, have covered Borwein’s Experimental Mathematics books so he has good connections with them.
5.2 Other publicity
6.1 The media If we are approached by the press, radio or television for biographical details, have you any objection to our providing them? We are happy to oblige
6.2 Media contacts Science journalists such as Dana Mackenzie, Barry Cipra, Ivars Petersen, Brian Hayes, Stephen Strauss and James Gleick have often covered Borwein’s more computational research.
6.4 Lecture tours/speaking engagements JMB is giving a plenary address at the 2009 December Winter Meeting of the CMS with title that of the book---there is an associated special session. He is also giving plenary lectures at two or three European meetings in 2009 celebrating Francis Clarke’s 60th birthday.
7.1 Bookshop If you have a bookshop where you are known, please supply details so that we may draw its attention to your book. Does Amazon count? Our own University bookshops?
8.1 Translation rights Borwein has had books translated into Russian, Japanese, Chinese (HK with and PRC without permission), Arabic, Indonesian, Italian. He could perhaps with effort work out by whom in every case. They include: Hong Kong (Owl Publishing), Indonesian (Erlanga Penerbit), Italian (Gremese Editore), Arabic (Academia International)
A few expository articles and chapters have been translated into German, Russian, Japanese, French, Italian, …
He is also actively involved translation in and from French translation grace of being Canadian and having overseen various CMS Book Series from 1991-2008 (with MAA, Wiley, Springer and AK Peters)..
8.2 Foreign publishers Have you contacts with any other foreign publishers who might be interested in publishing a translation ofthis book? See 8.1.
Do you know the name of a prominent academic in that country who is familiar with your work and who also might be prepared to endorse it for a foreign publisher?
Yes, along the lines of the previous answers: in most EU and Commonwealth countries, Israel, Chile, Brazil, China, Japan…. Borwein could probably find several such individuals.
9 Textbooks
9.1 Is your book suitable for main or supplementary use? In which semester/term is the course taught?
9.2 Subjects and departments In which departments are there likely to be courses for which your book may be adopted?