Convex Analysis and Nonlinear Optimization

Theory and Examples

  • Jonathan M. Borwein
  • Adrian S. Lewis

Table of contents

  1. Front Matter
    Pages i-x
  2. Jonathan M. Borwein, Adrian S. Lewis
    Pages 1-14
  3. Jonathan M. Borwein, Adrian S. Lewis
    Pages 15-32
  4. Jonathan M. Borwein, Adrian S. Lewis
    Pages 33-63
  5. Jonathan M. Borwein, Adrian S. Lewis
    Pages 65-96
  6. Jonathan M. Borwein, Adrian S. Lewis
    Pages 97-122
  7. Jonathan M. Borwein, Adrian S. Lewis
    Pages 123-152
  8. Jonathan M. Borwein, Adrian S. Lewis
    Pages 153-177
  9. Jonathan M. Borwein, Adrian S. Lewis
    Pages 179-208
  10. Jonathan M. Borwein, Adrian S. Lewis
    Pages 209-220
  11. Jonathan M. Borwein, Adrian S. Lewis
    Pages 221-240
  12. Back Matter
    Pages 241-273

About this book


A cornerstone of modern optimization and analysis, convexity pervades applications ranging through engineering and computation to finance.

This concise introduction to convex analysis and its extensions aims at first year graduate students, and includes many guided exercises. The corrected Second Edition adds a chapter emphasizing concrete models. New topics include monotone operator theory, Rademacher's theorem, proximal normal geometry, Chebyshev sets, and amenability. The final material on "partial smoothness" won a 2005 SIAM Outstanding Paper Prize.

Jonathan M. Borwein, FRSC is Canada Research Chair in Collaborative Technology at Dalhousie University. A Fellow of the AAAS and a foreign member of the Bulgarian Academy of Science, he received his Doctorate from Oxford in 1974 as a Rhodes Scholar and has worked at Waterloo, Carnegie Mellon and Simon Fraser Universities. Recognition for his extensive publications in optimization, analysis and computational mathematics includes the 1993 Chauvenet prize.


Adrian S. Lewis is a Professor in the School of Operations Research and Industrial Engineering at Cornell. Following his 1987 Doctorate from Cambridge, he has worked at Waterloo and Simon Fraser Universities. He received the 1995 Aisenstadt Prize, from the University of Montreal, and the 2003 Lagrange Prize for Continuous Optimization, from SIAM and the Mathematical Programming Society.


About the First Edition:


"...a very rewarding book, and I highly recommend it... "

- M.J. Todd, in the International Journal of Robust and Nonlinear Control


"...a beautifully written book... highly recommended..."

- L. Qi, in the Australian Mathematical Society Gazette


"This book represents a tour de force for introducing so many topics of present interest in such a small space and with such clarity and elegance."

- J.-P. Penot, in Canadian Mathematical Society Notes


"There is a fascinating interweaving of theory and applications..."

- J.R. Giles, in Mathematical Reviews

" ideal introductory teaching text..."

- S. Cobzas, in Studia Universitatis Babes-Bolyai Mathematica


Mathematica Microsoft Access PostScript boundary element method constraint convex analysis duality equality inequality linear optimization nonlinear optimization online optimization proof set

Authors and affiliations

  • Jonathan M. Borwein
    • 1
  • Adrian S. Lewis
    • 2
  1. 1.Centre for Experimental and Constructive Mathematics, Department of Mathematics and StatisticsSimon Fraser UniversityBurnabyCanada
  2. 2.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-9861-6
  • Online ISBN 978-1-4757-9859-3
  • Series Print ISSN 1613-5237
  • Buy this book on publisher's site