Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

This book starts with illustrations of the ubiquitous character of optimization, and describes numerical algorithms in a tutorial way. It covers fundamental algorithms as well as more specialized and advanced topics for unconstrained and constrained problems. This new edition of Numerical Optimization contains computational exercises in the form of case studies which help understanding optimization methods beyond their theoretical description when coming to actual implementation.

Convex Analysis may be considered as a refinement of standard calculus, with equalities and approximations replaced by inequalities. As such, it can easily be integrated into a graduate study curriculum. Minimization algorithms, more specifically those adapted to non-differentiable functions, provide an immediate application of convex analysis to various fields related to optimization and operations research. These two topics making up the title of the book, reflect the two origins of the authors, who belong respectively to the academic world and to that of applications. Part I can be used as an introductory textbook (as a basis for courses, or for self-study); Part II continues this at a higher technical level and is addressed more to specialists, collecting results that so far have not appeared in books.

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

From the reviews: "The account is quite detailed and is written in a manner that will appeal to analysts and numerical practitioners alike...they contain everything from rigorous proofs to tables of numerical calculations.... one of the strong features of these books...that they are designed not for the expert, but for those who whish to learn the subject matter starting from little or no background...there are numerous examples, and counter-examples, to back up the theory...To my knowledge, no other authors have given such a clear geometric account of convex analysis." "This innovative text is well written, copiously illustrated, and accessible to a wide audience"

This book is an abridged version of the two volumes "Convex Analysis and Minimization Algorithms I and II" (Grundlehren der mathematischen Wissenschaften Vol. 305 and 306), which presented an introduction to the basic concepts in convex analysis and a study of convex minimization problems. The "backbone" of both volumes was extracted, some material deleted that was deemed too advanced for an introduction, or too closely related to numerical algorithms. Some exercises were included and finally the index has been considerably enriched. The main motivation of the authors was to "light the entrance" of the monument Convex Analysis. This book is not a reference book to be kept on the shelf by experts who already know the building and can find their way through it; it is far more a book for the purpose of learning and teaching.

Ce livre est exclusivement consacre aux algorithmes numeriques d'optimisation (quasi-Newton, faisceaux, programmation quadratique successive, points interieurs); les bases theoriques (conditions d'optimalite, multiplicateurs de Lagrange) sont supposees connues.
Son but est de familiariser le lecteur avec ces algorithmes, qui sont pour la plupart bien classiques. Leur description insiste sur leur implementation numerique, ils peuvent etre programmes directement par un lecteur experimente. Le cote theorique n'est pas pour autant neglige, avec demonstration de chaque theoreme de convergence ou vitesse de convergence; souvent, ces demonstrations utilisent des hypotheses minimales.