Self-Regularity: A New Paradigm for Primal-Dual Interior-Point Algorithms
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
2002
|
| Schriftenreihe: | Princeton Series in Applied Mathematics
|
| Schlagworte: | |
| Online-Zugang: | FAB01 FAW01 FCO01 FHA01 FKE01 FLA01 UPA01 Volltext Volltext |
| Beschreibung: | Main description: Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work |
| Beschreibung: | 1 Online-Ressource (208 S.) |
| ISBN: | 9781400825134 |
| DOI: | 10.1515/9781400825134 |
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Datensatz im Suchindex
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| indexdate | 2024-07-10T01:24:00Z |
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| isbn | 9781400825134 |
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| spelling | Terlaky, Tamás Verfasser aut Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms Princeton, N.J. Princeton University Press 2002 1 Online-Ressource (208 S.) txt rdacontent c rdamedia cr rdacarrier Princeton Series in Applied Mathematics Main description: Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work Innerer Punkt (DE-588)4336760-4 gnd rswk-swf Konvexe Optimierung (DE-588)4137027-2 gnd rswk-swf Semidefinite Optimierung (DE-588)4663806-4 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Algorithmus (DE-588)4001183-5 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s Semidefinite Optimierung (DE-588)4663806-4 s Konvexe Optimierung (DE-588)4137027-2 s Innerer Punkt (DE-588)4336760-4 s Algorithmus (DE-588)4001183-5 s 1\p DE-604 Optimierung (DE-588)4043664-0 s 2\p DE-604 Peng, Jiming Sonstige oth Roos, Cornelis Sonstige oth https://doi.org/10.1515/9781400825134 Verlag Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400825134&searchTitles=true 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 | Terlaky, Tamás Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms Innerer Punkt (DE-588)4336760-4 gnd Konvexe Optimierung (DE-588)4137027-2 gnd Semidefinite Optimierung (DE-588)4663806-4 gnd Lineare Optimierung (DE-588)4035816-1 gnd Optimierung (DE-588)4043664-0 gnd Algorithmus (DE-588)4001183-5 gnd |
| subject_GND | (DE-588)4336760-4 (DE-588)4137027-2 (DE-588)4663806-4 (DE-588)4035816-1 (DE-588)4043664-0 (DE-588)4001183-5 |
| title | Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms |
| title_auth | Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms |
| title_exact_search | Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms |
| title_full | Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms |
| title_fullStr | Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms |
| title_full_unstemmed | Self-Regularity A New Paradigm for Primal-Dual Interior-Point Algorithms |
| title_short | Self-Regularity |
| title_sort | self regularity a new paradigm for primal dual interior point algorithms |
| title_sub | A New Paradigm for Primal-Dual Interior-Point Algorithms |
| topic | Innerer Punkt (DE-588)4336760-4 gnd Konvexe Optimierung (DE-588)4137027-2 gnd Semidefinite Optimierung (DE-588)4663806-4 gnd Lineare Optimierung (DE-588)4035816-1 gnd Optimierung (DE-588)4043664-0 gnd Algorithmus (DE-588)4001183-5 gnd |
| topic_facet | Innerer Punkt Konvexe Optimierung Semidefinite Optimierung Lineare Optimierung Optimierung Algorithmus |
| url | https://doi.org/10.1515/9781400825134 http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400825134&searchTitles=true |
| work_keys_str_mv | AT terlakytamas selfregularityanewparadigmforprimaldualinteriorpointalgorithms AT pengjiming selfregularityanewparadigmforprimaldualinteriorpointalgorithms AT rooscornelis selfregularityanewparadigmforprimaldualinteriorpointalgorithms |