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Practical Optimization

Philip E. Gill, Walter Murray, and Margaret H. Wright
Publication Date: 
Number of Pages: 
SIAM Classics
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Brian Borchers
, on
This book is a reprint edition of a book originally published by Academic Press in 1981.  For those familiar with the earlier edition, there does not appear to be any new material in this SIAM Classics edition.
The book covers the classical theory of smooth nonlinear optimization problems including the Karush-Kuhn-Tucker conditions and Lagrangian duality.  Methods for smooth unconstrained nonlinear optimization problems include Newton's method, quasi-Newton methods, limited-memory quasi-Newton methods, and the Levenberg-Marquardt method.  Methods for smooth constrained optimization problems include penalty and barrier function methods, reduced gradient methods, augmented Lagrangian methods, and sequential quadratic programming.  The book was published before the renaissance in interior-point methods in the 1990's.  Although the methods presented in this book are still widely used, there has been substantial progress over the last 40 years, and this material is somewhat out of date.  
Unlike many other books on nonlinear programming that were published in this era, Practical Optimization includes significant material on computational issues in nonlinear optimization, including numerical linear algebra (matrix factorizations and low-rank updates), scaling issues, finite difference derivatives, and optimality tolerances.  The authors were very familiar with these issues from their work with the MINOS solver at Stanford and some of this material is still relevant forty years after the original publication of the book.
This book will be of some interest as a reference on these practical numerical computing issues in nonlinear programming.  A more up-to-date reference that covers most of the theory and methods in this book but with less attention to numerical issues is Numerical Optimization by Jorge Nocedal and Stephen J. Wright. 


Brian Borchers is a Professor of Mathematics at New Mexico Tech and the editor of MAA Reviews.