Dual Prediction-Correction Methods for Linearly Constrained Time-Varying Convex Programs
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track the optimizer trajectory of the continuously-varying convex...
Gespeichert in:
| Veröffentlicht in: | IEEE transactions on automatic control Jg. 64; H. 8; S. 3355 - 3361 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
IEEE
01.08.2019
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Schlagworte: | |
| ISSN: | 0018-9286, 1558-2523 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track the optimizer trajectory of the continuously-varying convex optimization program. Recently, a novel prediction-correction methodology has been put forward to set up iterative algorithms that sample the continuously-varying optimization program at discrete time steps and perform a limited amount of computations to correct their approximate optimizer with the new sampled problem and predict how the optimizer will change at the next time step. Prediction-correction algorithms have been shown to outperform more classical strategies, i.e., correction-only methods. Typically, prediction-correction methods have asymptotical tracking errors of the order of <inline-formula><tex-math notation="LaTeX">h^2</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">h</tex-math></inline-formula> is the sampling period, whereas classical strategies have order of <inline-formula><tex-math notation="LaTeX">h</tex-math></inline-formula>. Up to now, prediction-correction algorithms have been developed in the primal space, both for unconstrained and simply constrained convex programs. In this paper, we show how to tackle linearly constrained continuously-varying problem by prediction-correction in the dual space and we prove similar asymptotical error bounds as their primal versions. |
|---|---|
| AbstractList | Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track the optimizer trajectory of the continuously-varying convex optimization program. Recently, a novel prediction–correction methodology has been put forward to set up iterative algorithms that sample the continuously-varying optimization program at discrete time steps and perform a limited amount of computations to correct their approximate optimizer with the new sampled problem and predict how the optimizer will change at the next time step. Prediction–correction algorithms have been shown to outperform more classical strategies, i.e., correction-only methods. Typically, prediction–correction methods have asymptotical tracking errors of the order of [Formula Omitted], where [Formula Omitted] is the sampling period, whereas classical strategies have order of [Formula Omitted]. Up to now, prediction–correction algorithms have been developed in the primal space, both for unconstrained and simply constrained convex programs. In this paper, we show how to tackle linearly constrained continuously-varying problem by prediction–correction in the dual space and we prove similar asymptotical error bounds as their primal versions. Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track the optimizer trajectory of the continuously-varying convex optimization program. Recently, a novel prediction-correction methodology has been put forward to set up iterative algorithms that sample the continuously-varying optimization program at discrete time steps and perform a limited amount of computations to correct their approximate optimizer with the new sampled problem and predict how the optimizer will change at the next time step. Prediction-correction algorithms have been shown to outperform more classical strategies, i.e., correction-only methods. Typically, prediction-correction methods have asymptotical tracking errors of the order of <inline-formula><tex-math notation="LaTeX">h^2</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">h</tex-math></inline-formula> is the sampling period, whereas classical strategies have order of <inline-formula><tex-math notation="LaTeX">h</tex-math></inline-formula>. Up to now, prediction-correction algorithms have been developed in the primal space, both for unconstrained and simply constrained convex programs. In this paper, we show how to tackle linearly constrained continuously-varying problem by prediction-correction in the dual space and we prove similar asymptotical error bounds as their primal versions. |
| Author | Simonetto, Andrea |
| Author_xml | – sequence: 1 givenname: Andrea orcidid: 0000-0003-2923-3361 surname: Simonetto fullname: Simonetto, Andrea email: andrea.simonetto@ibm.com organization: Optimization and Control Group of IBM Research Ireland, Dublin, Ireland |
| BookMark | eNp9UDtPwzAQtlCRaAs7Eksk5hTbiR8Zq_CUimAoiM1ynUtxlcbFThH99zi0YmBgujt9j9P3jdCgdS0gdE7whBBcXM2n5YRiIidUCsElPUJDwphMKaPZAA1xhNKCSn6CRiGs4snznAzR2_VWN8mzh8qazro2LZ338LMmj9C9uyoktfPJzLagfbNLSteGzut4VsncriF91X5n22UPfMJXtHJLr9fhFB3Xuglwdphj9HJ7My_v09nT3UM5naWGFqRLOZU1hYoUoGmhJdbVoja6zgHnOMsKscBQMMIEJlUVeWBqY0glMOOYU5wtsjG63PtuvPvYQujUym19G18qSrlgOc9YHll8zzLeheChVsZ2uk_ZZ2kUwapvUcUWVd-iOrQYhfiPcOPtOkb-T3Kxl1gA-KVLhqkQMvsGPCF_rQ |
| CODEN | IETAA9 |
| CitedBy_id | crossref_primary_10_1016_j_jfranklin_2024_106898 crossref_primary_10_1109_JAS_2024_124374 crossref_primary_10_1109_TAC_2024_3358099 crossref_primary_10_1109_LCSYS_2019_2930491 crossref_primary_10_1016_j_arcontrol_2023_100904 crossref_primary_10_1109_TCNS_2020_3020972 crossref_primary_10_1002_rnc_6157 crossref_primary_10_1109_TCSI_2022_3185398 crossref_primary_10_1016_j_automatica_2024_112107 crossref_primary_10_1109_TAC_2023_3335004 crossref_primary_10_1109_TIE_2024_3511137 crossref_primary_10_1109_TPWRS_2023_3276049 crossref_primary_10_1016_j_amc_2024_128712 crossref_primary_10_1109_TAC_2020_3010242 crossref_primary_10_1016_j_jclepro_2022_131935 crossref_primary_10_1109_JPROC_2020_3003156 crossref_primary_10_1016_j_ijepes_2021_107859 crossref_primary_10_1109_LCSYS_2023_3312297 crossref_primary_10_1007_s10851_024_01214_w crossref_primary_10_1109_TAC_2019_2917023 crossref_primary_10_1016_j_sigpro_2023_109089 crossref_primary_10_1109_TCNS_2023_3272220 crossref_primary_10_1109_JPROC_2025_3557698 crossref_primary_10_1109_LCSYS_2025_3582207 crossref_primary_10_1109_TAC_2024_3482977 crossref_primary_10_1109_TAC_2022_3190054 |
| Cites_doi | 10.1137/090762634 10.1109/TSP.2012.2222398 10.1109/TSP.2017.2728498 10.1137/16M1068736 10.1137/S0036144503423264 10.23919/ACC.2018.8431821 10.1137/120876915 10.1007/s10957-006-9080-1 10.1109/CDC.2016.7798732 10.1007/978-3-642-61257-2 10.1287/moor.5.1.43 10.1109/TAC.2017.2694611 10.1109/TAC.2017.2760256 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2019 |
| DBID | 97E RIA RIE AAYXX CITATION 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D |
| DOI | 10.1109/TAC.2018.2877682 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005–Present IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE/IET Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Technology Research Database |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE/IET Electronic Library (IEL) (UW System Shared) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1558-2523 |
| EndPage | 3361 |
| ExternalDocumentID | 10_1109_TAC_2018_2877682 8502778 |
| Genre | orig-research |
| GrantInformation_xml | – fundername: Milwaukee Hilton City Center |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACGFS ACIWK ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P RIA RIE RNS TAE TN5 VH1 VJK ~02 AAYXX CITATION 7SC 7SP 7TB 8FD FR3 JQ2 L7M L~C L~D RIG |
| ID | FETCH-LOGICAL-c291t-628f2ed19ea29a80adbfcaf4e0403397b0e9515701dd2edecfcc1d705606203b3 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 38 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000478694300023&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0018-9286 |
| IngestDate | Mon Jun 30 10:08:56 EDT 2025 Sat Nov 29 05:40:51 EST 2025 Tue Nov 18 22:43:12 EST 2025 Wed Aug 27 02:54:34 EDT 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html https://doi.org/10.15223/policy-029 https://doi.org/10.15223/policy-037 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c291t-628f2ed19ea29a80adbfcaf4e0403397b0e9515701dd2edecfcc1d705606203b3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-2923-3361 |
| PQID | 2267546354 |
| PQPubID | 85475 |
| PageCount | 7 |
| ParticipantIDs | ieee_primary_8502778 proquest_journals_2267546354 crossref_primary_10_1109_TAC_2018_2877682 crossref_citationtrail_10_1109_TAC_2018_2877682 |
| PublicationCentury | 2000 |
| PublicationDate | 2019-08-01 |
| PublicationDateYYYYMMDD | 2019-08-01 |
| PublicationDate_xml | – month: 08 year: 2019 text: 2019-08-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE transactions on automatic control |
| PublicationTitleAbbrev | TAC |
| PublicationYear | 2019 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref12 ref15 ref11 ref10 simonetto (ref14) 2017 polyak (ref7) 1987 ref2 ref1 ref16 ref8 simonetto (ref13) 2017 ref9 ref4 ref3 ref6 ref5 |
| References_xml | – ident: ref3 doi: 10.1137/090762634 – ident: ref12 doi: 10.1109/TSP.2012.2222398 – ident: ref5 doi: 10.1109/TSP.2017.2728498 – ident: ref10 doi: 10.1137/16M1068736 – ident: ref15 doi: 10.1137/S0036144503423264 – ident: ref1 doi: 10.23919/ACC.2018.8431821 – ident: ref9 doi: 10.1137/120876915 – ident: ref16 doi: 10.1007/s10957-006-9080-1 – year: 2017 ident: ref13 article-title: Time-Varying Convex Optimization via Time-Varying Averaged Operators – ident: ref6 doi: 10.1109/CDC.2016.7798732 – ident: ref11 doi: 10.1007/978-3-642-61257-2 – ident: ref8 doi: 10.1287/moor.5.1.43 – year: 2017 ident: ref14 article-title: Dual Prediction-Correction Methods for Linearly Constrained Time-Varying Convex Programs publication-title: 1709 05850 – ident: ref4 doi: 10.1109/TAC.2017.2694611 – year: 1987 ident: ref7 publication-title: Introduction to Optimization – ident: ref2 doi: 10.1109/TAC.2017.2760256 |
| SSID | ssj0016441 |
| Score | 2.516309 |
| Snippet | Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 3355 |
| SubjectTerms | Algorithms Asymptotic methods Asymptotic properties Computational geometry Convergence Convex analysis Convex functions Convexity Cost function Dual ascent Error correction Iterative algorithms Iterative methods Machine learning parametric programming Prediction algorithms prediction–correction methods Signal processing Signal processing algorithms time-varying convex optimization Tracking errors Trajectory Trajectory optimization |
| Title | Dual Prediction-Correction Methods for Linearly Constrained Time-Varying Convex Programs |
| URI | https://ieeexplore.ieee.org/document/8502778 https://www.proquest.com/docview/2267546354 |
| Volume | 64 |
| WOSCitedRecordID | wos000478694300023&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE/IET Electronic Library (IEL) (UW System Shared) customDbUrl: eissn: 1558-2523 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0016441 issn: 0018-9286 databaseCode: RIE dateStart: 19630101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8NAEB5UPOjBVxWrVXLwIpg22aTZ3WOpigctPdTSW9hkJyBIK33hz3dmE4OiCN4WMrssM7s732ReAFdaKLQizPxAioQMFLJZdRyib4URpJ5IQ7rcqvGjHAzUZKKHG3BT58Igogs-wzYPnS_fzvIV_yrrqC57HNUmbEopy1yt2mPAer18dekCC1W7JAPdGfX6HMOl2mQdELoW31SQ66ny4yF22uV-_3_7OoC9CkV6vVLsh7CB0yPY_VJbsAGT2xVRDOfsiGHm-33uw-GG3pNrG73wCLB6ZIwiFzn2uHWnaxiB1uPEEH9s5pwDxR_W-E5LuUiuxTE839-N-g9-1UbBz4UOl34iVCHQhhqN0EYFxmZFbooY6f5GBEeyAAlmdWUQWkt0mBd5HlpJyChIRBBl0QlsTWdTPAUvzGxmwq6JrYljnRHYScg-LKS1MouMSprQ-eRsmlc1xnnnr6mzNQKdkixSlkVayaIJ1_WMt7K-xh-0DeZ9TVexvQmtT-Gl1QVcpIQqJVf678Znv886hx1aW5exfC3YWs5XeAHb-Xr5sphfurP1AVxyy6U |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEB50FdSDb3F99uBFsG6T7SM5yqoorouHVfZW0mYKgqyyD_HnO5N2i6II3gKdtGGmyXyTeQGcaKnQSpH5QSJjMlDIZtWhQN9KI0k9kYZ0uVVP3aTXU4OBfpiDszoXBhFd8Bme89D58u1rPuWrspaK2OOo5mEhCkMpymyt2mfAmr08d2kLS1U7JQPd6l90OIpLnZN9QPhaflNCrqvKj6PY6Zfrtf-tbB1WKxzpXZSC34A5HG7CypfqglswuJwSxcOIXTHMfr_DnTjc0Lt3jaPHHkFWj8xR5DLHHjfvdC0j0HqcGuI_mRFnQfGDd_ygV7lYrvE2PF5f9Ts3ftVIwc-lFhM_lqqQaIVGI7VRgbFZkZsiRNrBbQIkWYAEtKIkENYSHeZFngubEDYKYhm0s_YONIavQ9wFT2Q2MyIyoTVhqDOCOzFZiEVibZK1jYqb0JpxNs2rKuO88pfUWRuBTkkWKcsirWTRhNN6xltZYeMP2i3mfU1Xsb0JBzPhpdUWHKeEKxOu9R-Fe7_POoalm_59N-3e9u72YZm-o8vIvgNoTEZTPITF_H3yPB4duf_sExvfzuw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Dual+Prediction%E2%80%93Correction+Methods+for+Linearly+Constrained+Time-Varying+Convex+Programs&rft.jtitle=IEEE+transactions+on+automatic+control&rft.au=Simonetto%2C+Andrea&rft.date=2019-08-01&rft.issn=0018-9286&rft.eissn=1558-2523&rft.volume=64&rft.issue=8&rft.spage=3355&rft.epage=3361&rft_id=info:doi/10.1109%2FTAC.2018.2877682&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_TAC_2018_2877682 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9286&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9286&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9286&client=summon |