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55816489
Introductory Lectures on Convex Optimization: Basic Course (Applied Optimization, 87)
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Nº de artículo:
55816489
BOB 1404
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The importance of Karmarkar's paper was not only in its complexity bound, but also the fact that its high efficiency was supported by excellent computational results, which dramatically changed the style and directions of research in nonlinear optimization.
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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.
| Publisher | Kluwer Academic Pub |
| Publication date | December 31, 2003 |
| Edition | 2004th |
| Language | English |
| Print length | 254 pages |
| ISBN-10 | 1402075537 |
| ISBN-13 | 978-1402075537 |
| Item Weight | 1.25 pounds (570 grams) |
| Dimensions | 6.25 x 1 x 10 inches (15.9 x 2.5 x 25.4 cm) |
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Introductory Lectures on Convex Optimization: Basic Course (Applied Optimization, 87)
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- Karmarkar's paper opened a new epoch in nonlinear optimization.
- The theoretical prediction of its high efficiency was supported by excellent computational results.
- New methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments.
- The new field was called polynomial-time interior-point methods.
- The author was challenged to reflect the new developments in the field in a new course on nonlinear optimization.
- Only the theory of interior-point methods for linear optimization was polished enough to be explained to students.
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