Introductory Lectures on Convex Optimization : A Basic Course PDF
by Y. Nesterov
Part of the Applied Optimization series
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It was in the middle of the 1980s, when the seminal paper by Kar- markar opened a new epoch in nonlinear optimization.
The importance of this paper, containing a new polynomial-time algorithm for linear op- timization problems, was not only in its complexity bound.
At that time, the most surprising feature of this algorithm was that the theoretical pre- diction of its high efficiency was supported by excellent computational results.
This unusual fact dramatically changed the style and direc- tions of the research in nonlinear optimization.
Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments.
In a new rapidly develop- ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory.
Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs[12, 14, 16, 17, 18, 19].
Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students.
The idea was to create a course which would reflect the new developments in the field.
Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students.
The general theory of self-concordant functions had appeared in print only once in the form of research monograph [12].
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- Format:PDF
- Publisher:Springer US
- Publication Date:01/12/2013
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- ISBN:9781441988539
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-
Download Now
- Format:PDF
- Publisher:Springer US
- Publication Date:01/12/2013
- Category:
- ISBN:9781441988539