VI Preface
for the simpler problems of linear and quadratic programming, and whose
application to more general situations is the subject of active research.
This book is a translated and improved version of the monograph [43],
written in French. The French monograph was used as the textbook of an
intensive two week course given several times by the authors, both in France
and abroad. Each topic was presented from a theoretical point of view in
morning lectures. The afternoons were devoted to implementation issues and
related computational work. The conception of such a course is due to J.-B.
Hiriart-Urruty, to whom the authors are deeply indebted.
Finally, three of the authors express their warm gratitude to Claude
Lemar´echal for having given the impetus to this new work by providing a
first English version.
Notes on this revised edition. Besides minor corrections, the present
version contains substantial changes with respect to the first edition. First
of all, (simplified but) nontrivial application problems have been inserted.
They involve the typical operations to be performed when one is faced with a
real-life application: modelling, choice of methodology and some theoretical
work to motivate it, computer implementation. Such computational exercises
help getting a better understanding of optimization methods beyond their
theoretical description, by addressing important features to be taken into
account when passing to implementation of any numerical algorithm.
In addition, the theoretical background in Part I now includes a discus-
sion on global convergence, and a section on the classical pivotal approach
to quadratic programming. Part II has been completely reorganized and ex-
panded. The introductory chapter, on basic subdifferential calculus and du-
ality theory, has two examples of nonsmooth functions that appear often in
practice and serve as motivation (pointwise maximum and dual functions).
A new section on convergence results for bundle methods has been added.
The chapter on applications of nonsmooth optimization, previously focusing
on decomposition of complex problems via Lagrangian duality, describes also
extensions of bundle methods for handling varying dimensions, for solving
constrained problems, and for solving generalized equations. Also, a brief
commented review of existing software for nonlinear optimization has been
added in Part III.
Finally, the reader will find additional information at http://www-rocq.
inria.fr/~gilbert/bgls. The page gathers the data for running the test
problems, various optimization codes, including an SQP solver (in Matlab),
and pieces of software that solve the computational exercises.
Paris, Grenoble, Rio de Janeiro, J. Fr´ed´eric Bonnans
May 2006 J. Charles Gilbert
Claude Lemar´echal
Claudia A. Sagastiz´abal
sstoney2013-03-01Bonnas的数值优化书，比较详细，文字图片都很清楚
