Central Swaths
Abstract We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically...
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| Autor*in: |
Renegar, James [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© SFoCM 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Foundations of computational mathematics - Springer-Verlag, 2001, 13(2013), 3 vom: 30. März, Seite 405-454 |
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| Übergeordnetes Werk: |
volume:13 ; year:2013 ; number:3 ; day:30 ; month:03 ; pages:405-454 |
| Links: |
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| DOI / URN: |
10.1007/s10208-013-9148-x |
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| 520 | |a Abstract We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path. | ||
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10.1007/s10208-013-9148-x doi (DE-627)OLC2057961621 (DE-He213)s10208-013-9148-x-p DE-627 ger DE-627 rakwb eng 510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Renegar, James verfasserin aut Central Swaths 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © SFoCM 2013 Abstract We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path. Hyperbolicity cone Hyperbolic polynomial Hyperbolic programming Central path Conic programming Convex optimization Enthalten in Foundations of computational mathematics Springer-Verlag, 2001 13(2013), 3 vom: 30. März, Seite 405-454 (DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 1615-3375 nnns volume:13 year:2013 number:3 day:30 month:03 pages:405-454 https://doi.org/10.1007/s10208-013-9148-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 31.76$jNumerische Mathematik VZ 106408194 (DE-625)106408194 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 13 2013 3 30 03 405-454 |
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10.1007/s10208-013-9148-x doi (DE-627)OLC2057961621 (DE-He213)s10208-013-9148-x-p DE-627 ger DE-627 rakwb eng 510 004 VZ 510 VZ 17,1 ssgn 31.76$jNumerische Mathematik bkl 54.10$jTheoretische Informatik bkl Renegar, James verfasserin aut Central Swaths 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © SFoCM 2013 Abstract We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path. Hyperbolicity cone Hyperbolic polynomial Hyperbolic programming Central path Conic programming Convex optimization Enthalten in Foundations of computational mathematics Springer-Verlag, 2001 13(2013), 3 vom: 30. März, Seite 405-454 (DE-627)330598139 (DE-600)2050531-0 (DE-576)094479291 1615-3375 nnns volume:13 year:2013 number:3 day:30 month:03 pages:405-454 https://doi.org/10.1007/s10208-013-9148-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2088 GBV_ILN_4277 31.76$jNumerische Mathematik VZ 106408194 (DE-625)106408194 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 13 2013 3 30 03 405-454 |
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Central Swaths |
| abstract |
Abstract We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path. © SFoCM 2013 |
| abstractGer |
Abstract We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path. © SFoCM 2013 |
| abstract_unstemmed |
Abstract We develop a natural generalization to the notion of the central path, a concept that lies at the heart of interior-point methods for convex optimization. The generalization is accomplished via the “derivative cones” of a “hyperbolicity cone”, the derivatives being direct and mathematically appealing relaxations of the underlying (hyperbolic) conic constraint, be it the non-negative orthant, the cone of positive semidefinite matrices, or other. We prove that a dynamics inherent to the derivative cones generates paths always leading to optimality, the central path arising from a special case in which the derivative cones are quadratic. Derivative cones of higher degree better fit the underlying conic constraint, raising the prospect that the paths they generate lead to optimality quicker than the central path. © SFoCM 2013 |
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Central Swaths |
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https://doi.org/10.1007/s10208-013-9148-x |
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2024-07-03T17:02:54.740Z |
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