Non-Convex Distributed Optimization
We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization....
Ausführliche Beschreibung
Autor*in: |
Tatarenko, Tatiana [verfasserIn] |
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Artikel |
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Sprache: |
Englisch |
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2017 |
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Übergeordnetes Werk: |
Enthalten in: IEEE transactions on automatic control - New York, NY : Inst., 1963, 62(2017), 8, Seite 3744-3757 |
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Übergeordnetes Werk: |
volume:62 ; year:2017 ; number:8 ; pages:3744-3757 |
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DOI / URN: |
10.1109/TAC.2017.2648041 |
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OLC1995746800 |
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520 | |a We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. | ||
650 | 4 | |a Protocols | |
650 | 4 | |a Approximation algorithms | |
650 | 4 | |a Convergence | |
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10.1109/TAC.2017.2648041 doi PQ20171125 (DE-627)OLC1995746800 (DE-599)GBVOLC1995746800 (PRQ)c1064-b06c1884ad89d016a899d21b5d9c9b110616def9ee0a32824d89dd7029f70ad20 (KEY)0005057120170000062000803744nonconvexdistributedoptimization DE-627 ger DE-627 rakwb eng 620 DNB Tatarenko, Tatiana verfasserin aut Non-Convex Distributed Optimization 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. Protocols Approximation algorithms Convergence Heuristic algorithms Linear programming Algorithm design and analysis Non-convex optimization time-varying multi-agent Optimization Touri, Behrouz oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 8, Seite 3744-3757 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:8 pages:3744-3757 http://dx.doi.org/10.1109/TAC.2017.2648041 Volltext http://ieeexplore.ieee.org/document/7807315 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 8 3744-3757 |
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10.1109/TAC.2017.2648041 doi PQ20171125 (DE-627)OLC1995746800 (DE-599)GBVOLC1995746800 (PRQ)c1064-b06c1884ad89d016a899d21b5d9c9b110616def9ee0a32824d89dd7029f70ad20 (KEY)0005057120170000062000803744nonconvexdistributedoptimization DE-627 ger DE-627 rakwb eng 620 DNB Tatarenko, Tatiana verfasserin aut Non-Convex Distributed Optimization 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. Protocols Approximation algorithms Convergence Heuristic algorithms Linear programming Algorithm design and analysis Non-convex optimization time-varying multi-agent Optimization Touri, Behrouz oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 8, Seite 3744-3757 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:8 pages:3744-3757 http://dx.doi.org/10.1109/TAC.2017.2648041 Volltext http://ieeexplore.ieee.org/document/7807315 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 8 3744-3757 |
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10.1109/TAC.2017.2648041 doi PQ20171125 (DE-627)OLC1995746800 (DE-599)GBVOLC1995746800 (PRQ)c1064-b06c1884ad89d016a899d21b5d9c9b110616def9ee0a32824d89dd7029f70ad20 (KEY)0005057120170000062000803744nonconvexdistributedoptimization DE-627 ger DE-627 rakwb eng 620 DNB Tatarenko, Tatiana verfasserin aut Non-Convex Distributed Optimization 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. Protocols Approximation algorithms Convergence Heuristic algorithms Linear programming Algorithm design and analysis Non-convex optimization time-varying multi-agent Optimization Touri, Behrouz oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 8, Seite 3744-3757 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:8 pages:3744-3757 http://dx.doi.org/10.1109/TAC.2017.2648041 Volltext http://ieeexplore.ieee.org/document/7807315 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 8 3744-3757 |
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10.1109/TAC.2017.2648041 doi PQ20171125 (DE-627)OLC1995746800 (DE-599)GBVOLC1995746800 (PRQ)c1064-b06c1884ad89d016a899d21b5d9c9b110616def9ee0a32824d89dd7029f70ad20 (KEY)0005057120170000062000803744nonconvexdistributedoptimization DE-627 ger DE-627 rakwb eng 620 DNB Tatarenko, Tatiana verfasserin aut Non-Convex Distributed Optimization 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. Protocols Approximation algorithms Convergence Heuristic algorithms Linear programming Algorithm design and analysis Non-convex optimization time-varying multi-agent Optimization Touri, Behrouz oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 8, Seite 3744-3757 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:8 pages:3744-3757 http://dx.doi.org/10.1109/TAC.2017.2648041 Volltext http://ieeexplore.ieee.org/document/7807315 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 8 3744-3757 |
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10.1109/TAC.2017.2648041 doi PQ20171125 (DE-627)OLC1995746800 (DE-599)GBVOLC1995746800 (PRQ)c1064-b06c1884ad89d016a899d21b5d9c9b110616def9ee0a32824d89dd7029f70ad20 (KEY)0005057120170000062000803744nonconvexdistributedoptimization DE-627 ger DE-627 rakwb eng 620 DNB Tatarenko, Tatiana verfasserin aut Non-Convex Distributed Optimization 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. Protocols Approximation algorithms Convergence Heuristic algorithms Linear programming Algorithm design and analysis Non-convex optimization time-varying multi-agent Optimization Touri, Behrouz oth Enthalten in IEEE transactions on automatic control New York, NY : Inst., 1963 62(2017), 8, Seite 3744-3757 (DE-627)129601705 (DE-600)241443-0 (DE-576)015095320 0018-9286 nnns volume:62 year:2017 number:8 pages:3744-3757 http://dx.doi.org/10.1109/TAC.2017.2648041 Volltext http://ieeexplore.ieee.org/document/7807315 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-MAT GBV_ILN_11 GBV_ILN_70 GBV_ILN_120 GBV_ILN_193 GBV_ILN_2014 GBV_ILN_2016 GBV_ILN_2333 GBV_ILN_4193 AR 62 2017 8 3744-3757 |
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10.1109/TAC.2017.2648041 |
dewey-full |
620 |
title_sort |
non-convex distributed optimization |
title_auth |
Non-Convex Distributed Optimization |
abstract |
We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. |
abstractGer |
We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. |
abstract_unstemmed |
We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. The perturbed push-sum algorithm was previously used for convex distributed optimization. We generalize the result obtained for the convex case to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function, if the objective function has no saddle points. Our analysis shows that this perturbed procedure converges at a rate of <inline-formula><tex-math notation="LaTeX">O(1/t)</tex-math> </inline-formula>. |
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container_issue |
8 |
title_short |
Non-Convex Distributed Optimization |
url |
http://dx.doi.org/10.1109/TAC.2017.2648041 http://ieeexplore.ieee.org/document/7807315 |
remote_bool |
false |
author2 |
Touri, Behrouz |
author2Str |
Touri, Behrouz |
ppnlink |
129601705 |
mediatype_str_mv |
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isOA_txt |
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hochschulschrift_bool |
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author2_role |
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doi_str |
10.1109/TAC.2017.2648041 |
up_date |
2024-07-03T22:37:27.047Z |
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1803599213543555072 |
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