Introductory Lectures on Convex Optimization: A Basic Course
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Boston, MA
Springer US
2004
|
| Series: | Applied Optimization
87 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | It was in the middle of the 1980s, when the seminal paper by Karmarkar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear optimization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical prediction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and directions 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 developing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. After almost 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] |
| Physical Description: | 1 Online-Ressource (XVIII, 236 p) |
| ISBN: | 9781441988539 9781461346913 |
| ISSN: | 1384-6485 |
| DOI: | 10.1007/978-1-4419-8853-9 |
Staff View
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| 500 | |a It was in the middle of the 1980s, when the seminal paper by Karmarkar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear optimization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical prediction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and directions 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 developing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. After almost 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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| isbn | 9781441988539 9781461346913 |
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| language | English |
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| spelling | Nesterov, Yurii Verfasser aut Introductory Lectures on Convex Optimization A Basic Course by Yurii Nesterov Boston, MA Springer US 2004 1 Online-Ressource (XVIII, 236 p) txt rdacontent c rdamedia cr rdacarrier Applied Optimization 87 1384-6485 It was in the middle of the 1980s, when the seminal paper by Karmarkar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear optimization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical prediction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and directions 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 developing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. After almost 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] Mathematics Information theory Mathematical optimization Optimization Theory of Computation Mathematik Berechnungskomplexität (DE-588)4134751-1 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Konvexe Optimierung (DE-588)4137027-2 s Berechnungskomplexität (DE-588)4134751-1 s 2\p DE-604 Applied Optimization 87 (DE-604)BV010841718 87 https://doi.org/10.1007/978-1-4419-8853-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Nesterov, Yurii Introductory Lectures on Convex Optimization A Basic Course Applied Optimization Mathematics Information theory Mathematical optimization Optimization Theory of Computation Mathematik Berechnungskomplexität (DE-588)4134751-1 gnd Konvexe Optimierung (DE-588)4137027-2 gnd |
| subject_GND | (DE-588)4134751-1 (DE-588)4137027-2 (DE-588)4151278-9 |
| title | Introductory Lectures on Convex Optimization A Basic Course |
| title_auth | Introductory Lectures on Convex Optimization A Basic Course |
| title_exact_search | Introductory Lectures on Convex Optimization A Basic Course |
| title_full | Introductory Lectures on Convex Optimization A Basic Course by Yurii Nesterov |
| title_fullStr | Introductory Lectures on Convex Optimization A Basic Course by Yurii Nesterov |
| title_full_unstemmed | Introductory Lectures on Convex Optimization A Basic Course by Yurii Nesterov |
| title_short | Introductory Lectures on Convex Optimization |
| title_sort | introductory lectures on convex optimization a basic course |
| title_sub | A Basic Course |
| topic | Mathematics Information theory Mathematical optimization Optimization Theory of Computation Mathematik Berechnungskomplexität (DE-588)4134751-1 gnd Konvexe Optimierung (DE-588)4137027-2 gnd |
| topic_facet | Mathematics Information theory Mathematical optimization Optimization Theory of Computation Mathematik Berechnungskomplexität Konvexe Optimierung Einführung |
| url | https://doi.org/10.1007/978-1-4419-8853-9 |
| volume_link | (DE-604)BV010841718 |
| work_keys_str_mv | AT nesterovyurii introductorylecturesonconvexoptimizationabasiccourse |