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Fundamentals of Convex Analysis (Grundlehren Text Editions) (Englisch) Gebundene Ausgabe – 4. Oktober 2013


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From the reviews of the first edition:

"...This book is an abridged version of the book "Convex Analysis and Minimization Algorithms" (shortly CAMA) written in two volumes by the same authors... . The authors have extracted from CAMA Chapters III-VI and X, containing the fundamentals of convex analysis, deleting material seemed too advanced for an introduction, or too closely attached to numerical algorithms. Each Chapter is presented as a "lesson" treating a given subject in its entirety, completed by numerous examples and figures. So, this new version becomes a good book for learning and teaching of convex analysis in finite dimensions...."

S. Mititelu in "Zentralblatt für Mathematik und ihre Grenzgebiete", 2002

"I believe that the book under review will become the standard text doing much to implement the type of course Victor Klee was advocating and covering as it does the considerable recent development of the subject. … If you are looking for a well-designed text for a course on convex analysis, preliminary to one on optimization or nonlinear analysis then this is the one which will certainly be a standard for many years." (John Giles, The Australian Mathematical Society Gazette, Vol. 29 (2), 2002)

Synopsis

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.

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