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....
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| Autor*in: |
Tatarenko, Tatiana [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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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 |
| Links: |
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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 | |
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| 650 | 4 | |a Convergence | |
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| 650 | 4 | |a Algorithm design and analysis | |
| 650 | 4 | |a Non-convex optimization | |
| 650 | 4 | |a time-varying multi-agent | |
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| 700 | 1 | |a Touri, Behrouz |4 oth | |
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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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eng |
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Tatarenko, Tatiana |
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Tatarenko, Tatiana |
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10.1109/TAC.2017.2648041 |
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620 |
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non-convex distributed optimization |
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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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| title_short |
Non-Convex Distributed Optimization |
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http://dx.doi.org/10.1109/TAC.2017.2648041 http://ieeexplore.ieee.org/document/7807315 |
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2024-07-03T22:37:27.047Z |
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