Asymptotic convergence of constrained primal–dual dynamics
This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing...
Saved in:
| Published in | Systems & control letters Vol. 87; no. C; pp. 10 - 15 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Netherlands
Elsevier B.V
01.01.2016
Elsevier |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer. |
|---|---|
| AbstractList | This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal–dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal–dual optimizers are globally asymptotically stable under the primal–dual dynamics and that each solution of the dynamics converges to an optimizer. |
| Author | Mallada, Enrique Cherukuri, Ashish Cortés, Jorge |
| Author_xml | – sequence: 1 givenname: Ashish surname: Cherukuri fullname: Cherukuri, Ashish email: acheruku@ucsd.edu organization: Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA – sequence: 2 givenname: Enrique orcidid: 0000-0003-1568-1833 surname: Mallada fullname: Mallada, Enrique email: mallada@caltech.edu organization: Department of Computational and Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA – sequence: 3 givenname: Jorge surname: Cortés fullname: Cortés, Jorge email: cortes@ucsd.edu organization: Department of Mechanical and Aerospace Engineering, University of California, San Diego, CA 92093, USA |
| BackLink | https://www.osti.gov/biblio/1556180$$D View this record in Osti.gov |
| BookMark | eNqFkM1KAzEUhYNUsK2-ghT3MyaZSWYKXViKf1Bw032IyR1NmSYliYXZ-Q6-oU9iYnXjxtXlXs45nPtN0Mg6CwhdElwSTPj1tgxDUM72UFJMWDqWGPMTNCZtQ4tmzvgIjZOwKfickDM0CWGLMaa4qsZosQzDbh9dNGqWMg7gX8AqmLkuryF6aSzo2d6bnew_3z_0m-xnerByZ1Q4R6ed7ANc_Mwp2tzdblYPxfrp_nG1XBeqZlUstG4x1KStGICqJa2apmZacqlgTjmt4BkYoxoodFIq3EJDcNfWtCU1wVJVU3R1jHUhGhGUiaBeUzsLKgrCGCctTqLFUaS8C8FDJ5JORuNs_qEXBItMS2zFLy2RaeV7opXs_I_9-2U__G-8ORohATgY8LlgRqiNz_20M_9FfAE0DI0g |
| CitedBy_id | crossref_primary_10_1016_j_sysconle_2020_104754 crossref_primary_10_1109_TCNS_2020_2972590 crossref_primary_10_1016_j_automatica_2019_108712 crossref_primary_10_1109_LCSYS_2017_2750480 crossref_primary_10_1109_TAC_2018_2867589 crossref_primary_10_1109_TIA_2021_3114388 crossref_primary_10_1016_j_automatica_2017_07_022 crossref_primary_10_1016_j_automatica_2021_109585 crossref_primary_10_1016_j_automatica_2021_109660 crossref_primary_10_1016_j_sysconle_2017_07_014 crossref_primary_10_1109_TAC_2017_2713529 crossref_primary_10_1016_j_ifacol_2020_12_1254 crossref_primary_10_1109_TCSI_2024_3426313 crossref_primary_10_20965_jrm_2023_p0298 crossref_primary_10_1137_15M1026924 crossref_primary_10_1109_TAC_2021_3056233 crossref_primary_10_1109_TPWRS_2021_3109024 crossref_primary_10_1016_j_apenergy_2023_120764 crossref_primary_10_1109_TAC_2020_3019381 crossref_primary_10_1109_TCYB_2021_3104044 crossref_primary_10_1155_2016_7094157 crossref_primary_10_1002_rnc_6077 crossref_primary_10_1016_j_ifacol_2018_12_016 crossref_primary_10_1007_s11590_022_01910_9 crossref_primary_10_1016_j_ifacol_2015_10_207 crossref_primary_10_1109_TAC_2020_3019375 crossref_primary_10_1109_TAC_2020_3045124 crossref_primary_10_1109_TAC_2019_2927328 crossref_primary_10_1007_s11071_019_05376_w crossref_primary_10_1137_18M1229225 crossref_primary_10_1016_j_ijepes_2021_107934 crossref_primary_10_1016_j_neucom_2020_05_006 crossref_primary_10_1016_j_automatica_2018_09_004 crossref_primary_10_1016_j_sysconle_2025_106030 crossref_primary_10_1016_j_ifacol_2017_12_039 crossref_primary_10_1109_ACCESS_2019_2937448 crossref_primary_10_1109_TSG_2023_3303178 crossref_primary_10_2200_S00778ED1V01Y201705CNT018 crossref_primary_10_1109_TCNS_2023_3333400 crossref_primary_10_9746_sicetr_58_481 crossref_primary_10_1109_TAC_2017_2778689 crossref_primary_10_1080_00207721_2022_2141594 crossref_primary_10_1109_TAC_2016_2613901 crossref_primary_10_1088_1742_6596_1016_1_012012 crossref_primary_10_1109_LCSYS_2019_2916250 crossref_primary_10_1109_LCSYS_2020_2989372 crossref_primary_10_1109_TAC_2022_3176527 crossref_primary_10_1109_TCYB_2018_2883095 crossref_primary_10_1137_140967106 crossref_primary_10_1049_rpg2_12784 crossref_primary_10_1016_j_sysconle_2021_104894 crossref_primary_10_1016_j_ifacol_2023_10_755 crossref_primary_10_1109_TCYB_2020_2984516 crossref_primary_10_1016_j_automatica_2020_109003 crossref_primary_10_1109_LCSYS_2020_3037876 crossref_primary_10_1109_LCSYS_2024_3368008 crossref_primary_10_1109_TAC_2018_2823264 crossref_primary_10_1016_j_ifacol_2020_12_1110 crossref_primary_10_1109_TCNS_2018_2864140 crossref_primary_10_9746_sicetr_56_106 crossref_primary_10_1109_TNNLS_2022_3208086 crossref_primary_10_1109_TAC_2017_2752001 crossref_primary_10_1109_TCYB_2022_3179519 crossref_primary_10_1016_j_apenergy_2023_120864 crossref_primary_10_1016_j_ifacol_2020_12_1559 crossref_primary_10_1109_TAC_2017_2760256 crossref_primary_10_1016_j_automatica_2016_08_007 crossref_primary_10_1109_TCNS_2019_2915626 crossref_primary_10_1109_TAC_2023_3335004 crossref_primary_10_1145_3152042_3152071 crossref_primary_10_1109_LCSYS_2019_2918095 crossref_primary_10_1109_TCNS_2017_2648503 crossref_primary_10_1109_TSG_2017_2731811 crossref_primary_10_1109_TPWRS_2017_2682235 crossref_primary_10_1137_18M1234795 crossref_primary_10_1080_18824889_2023_2176154 crossref_primary_10_1109_TNET_2022_3156530 crossref_primary_10_1016_j_automatica_2019_108548 crossref_primary_10_1016_j_automatica_2022_110746 crossref_primary_10_1109_TAC_2019_2955031 crossref_primary_10_1109_TPWRS_2019_2931685 crossref_primary_10_9746_sicetr_55_286 crossref_primary_10_9746_jcmsi_13_299 crossref_primary_10_1016_j_automatica_2020_109311 crossref_primary_10_1051_smdo_2019010 crossref_primary_10_1109_TCST_2018_2816902 crossref_primary_10_1016_j_arcontrol_2024_100941 crossref_primary_10_1109_TWC_2024_3404231 crossref_primary_10_1016_j_ifacol_2020_12_1561 crossref_primary_10_1109_ACCESS_2019_2925053 crossref_primary_10_1109_LCSYS_2018_2851375 crossref_primary_10_1109_LCSYS_2020_3006822 crossref_primary_10_1051_cocv_2022032 crossref_primary_10_1007_s10107_023_02051_2 crossref_primary_10_1109_JAS_2023_123126 crossref_primary_10_1109_TPWRS_2021_3132348 |
| Cites_doi | 10.1016/j.automatica.2010.08.011 10.1109/Allerton.2013.6736511 10.1109/TNET.2013.2251896 10.1109/TAC.2014.2298140 10.1007/s00498-004-0145-0 10.1016/j.automatica.2005.10.014 10.1109/TSP.2011.2169407 10.1109/TAC.2002.806650 10.1109/37.980245 10.1109/ACC.2014.6858966 10.1109/ALLERTON.2014.7028527 10.2307/1905259 10.1109/TAC.2003.822858 |
| ContentType | Journal Article |
| Copyright | 2015 Elsevier B.V. |
| Copyright_xml | – notice: 2015 Elsevier B.V. |
| DBID | AAYXX CITATION OTOTI |
| DOI | 10.1016/j.sysconle.2015.10.006 |
| DatabaseName | CrossRef OSTI.GOV |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1872-7956 |
| EndPage | 15 |
| ExternalDocumentID | 1556180 10_1016_j_sysconle_2015_10_006 S0167691115002078 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 123 1B1 1RT 1~. 1~5 29Q 4.4 457 4G. 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AAAKG AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AARIN AAXUO ABFNM ABJNI ABMAC ABTAH ABUCO ABXDB ABYKQ ACDAQ ACGFS ACNNM ACRLP ADBBV ADEZE ADIYS ADMUD ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AIEXJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ APLSM ASPBG AVWKF AXJTR AZFZN BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HAMUX HVGLF HZ~ IHE J1W JJJVA KOM LY1 LY7 M41 MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG ROL RPZ SDF SDG SDP SDS SES SET SEW SPC SPCBC SSB SSD SST SSZ T5K TN5 WH7 WUQ XPP ZMT ZY4 ~G- AATTM AAXKI AAYWO AAYXX ABWVN ACRPL ACVFH ADCNI ADNMO AEIPS AEUPX AFJKZ AFPUW AFXIZ AGCQF AGQPQ AGRNS AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP BNPGV CITATION SSH AALMO ABPIF ABPTK OTOTI |
| ID | FETCH-LOGICAL-c453t-dd80e41835eec4a237745da6ace92623ebe552de2efaac08e710f84281410ac3 |
| IEDL.DBID | .~1 |
| ISSN | 0167-6911 |
| IngestDate | Mon Jul 24 03:56:23 EDT 2023 Tue Jul 01 03:29:06 EDT 2025 Thu Apr 24 23:02:12 EDT 2025 Fri Feb 23 02:32:49 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | C |
| Keywords | Discontinuous dynamics Primal–dual dynamics Caratheodory solutions Saddle points Constrained optimization |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c453t-dd80e41835eec4a237745da6ace92623ebe552de2efaac08e710f84281410ac3 |
| Notes | USDOE AC52-06NA25396 |
| ORCID | 0000-0003-1568-1833 0000000315681833 |
| OpenAccessLink | https://doi.org/10.1016/j.sysconle.2015.10.006 |
| PageCount | 6 |
| ParticipantIDs | osti_scitechconnect_1556180 crossref_citationtrail_10_1016_j_sysconle_2015_10_006 crossref_primary_10_1016_j_sysconle_2015_10_006 elsevier_sciencedirect_doi_10_1016_j_sysconle_2015_10_006 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | January 2016 2016-01-00 2016-01-01 |
| PublicationDateYYYYMMDD | 2016-01-01 |
| PublicationDate_xml | – month: 01 year: 2016 text: January 2016 |
| PublicationDecade | 2010 |
| PublicationPlace | Netherlands |
| PublicationPlace_xml | – name: Netherlands |
| PublicationTitle | Systems & control letters |
| PublicationYear | 2016 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Boyd, Vandenberghe (br000085) 2009 Ferragut, Paganini (br000025) 2014; 22 Lygeros, Johansson, Simić, Zhang, Sastry (br000055) 2003; 48 Bacciotti, Ceragioli (br000065) 2006; 42 Kose (br000010) 1956; 24 Brogliato, Goeleven (br000090) 2005; 17 Wen, Arcak (br000095) 2004; 49 Zhao, Topcu, Li, Low (br000035) 2014; 59 Arrow, Hurwitz, Uzawa (br000005) 1958 Low, Paganini, Doyle (br000100) 2002; 22 E. Mallada, C. Zhao, S. Low, Optimal load-side control for frequency regulation in smart grids, in: Allerton Conf. on Communications, Control and Computing, Monticello, IL, 2014, pp. 731–738. Feijer, Paganini (br000015) 2010; 46 Cortés (br000070) 2008; 28 Chen, Lau (br000020) 2012; 60 X. Zhang, A. Papachristodoulou, Distributed dynamic feedback control for smart power networks with tree topology, in: American Control Conference, Portland, OR, 2014, pp. 1156–1161. Khalil (br000050) 2002 Rudin (br000075) 1953 X. Ma, N. Elia, A distributed continuous-time gradient dynamics approach for the active power loss minimizations, in: Allerton Conf. on Communications, Control and Computing, Monticello, IL, 2013, pp. 100–106. Clarke (br000080) 1983 Nagurney, Zhang (br000060) 1996; vol.~2 Chen (10.1016/j.sysconle.2015.10.006_br000020) 2012; 60 Bacciotti (10.1016/j.sysconle.2015.10.006_br000065) 2006; 42 Kose (10.1016/j.sysconle.2015.10.006_br000010) 1956; 24 Clarke (10.1016/j.sysconle.2015.10.006_br000080) 1983 Zhao (10.1016/j.sysconle.2015.10.006_br000035) 2014; 59 Low (10.1016/j.sysconle.2015.10.006_br000100) 2002; 22 Lygeros (10.1016/j.sysconle.2015.10.006_br000055) 2003; 48 Boyd (10.1016/j.sysconle.2015.10.006_br000085) 2009 Feijer (10.1016/j.sysconle.2015.10.006_br000015) 2010; 46 10.1016/j.sysconle.2015.10.006_br000040 10.1016/j.sysconle.2015.10.006_br000030 Rudin (10.1016/j.sysconle.2015.10.006_br000075) 1953 10.1016/j.sysconle.2015.10.006_br000045 Brogliato (10.1016/j.sysconle.2015.10.006_br000090) 2005; 17 Nagurney (10.1016/j.sysconle.2015.10.006_br000060) 1996; vol.~2 Khalil (10.1016/j.sysconle.2015.10.006_br000050) 2002 Cortés (10.1016/j.sysconle.2015.10.006_br000070) 2008; 28 Ferragut (10.1016/j.sysconle.2015.10.006_br000025) 2014; 22 Wen (10.1016/j.sysconle.2015.10.006_br000095) 2004; 49 Arrow (10.1016/j.sysconle.2015.10.006_br000005) 1958 |
| References_xml | – volume: 24 start-page: 59 year: 1956 end-page: 70 ident: br000010 article-title: Solutions of saddle value problems by differential equations publication-title: Econometrica – volume: 17 start-page: 57 year: 2005 end-page: 76 ident: br000090 article-title: The Krakovskii-LaSalle invariance principle for a class of unilateral dynamical systems publication-title: Math. Control Signals Syst. – year: 1958 ident: br000005 article-title: Studies in Linear and Non-Linear Programming – volume: 28 start-page: 36 year: 2008 end-page: 73 ident: br000070 article-title: Discontinuous dynamical systems—a tutorial on solutions, nonsmooth analysis, and stability publication-title: IEEE Control Syst. Mag. – year: 1983 ident: br000080 article-title: Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts – year: 2009 ident: br000085 article-title: Convex Optimization – reference: E. Mallada, C. Zhao, S. Low, Optimal load-side control for frequency regulation in smart grids, in: Allerton Conf. on Communications, Control and Computing, Monticello, IL, 2014, pp. 731–738. – volume: 48 start-page: 2 year: 2003 end-page: 17 ident: br000055 article-title: Dynamical properties of hybrid automata publication-title: IEEE Trans. Automat. Control – volume: 22 start-page: 28 year: 2002 end-page: 43 ident: br000100 article-title: Internet congestion control publication-title: IEEE Control Syst. Mag. – volume: 46 start-page: 1974 year: 2010 end-page: 1981 ident: br000015 article-title: Stability of primal–dual gradient dynamics and applications to network optimization publication-title: Automatica – volume: vol.~2 year: 1996 ident: br000060 article-title: Projected dynamical systems and variational inequalities with applications publication-title: International Series in Operations Research and Management Science – volume: 49 start-page: 162 year: 2004 end-page: 174 ident: br000095 article-title: A unifying passivity framework for network flow control publication-title: IEEE Trans. Automat. Control – volume: 22 start-page: 349 year: 2014 end-page: 362 ident: br000025 article-title: Network resource allocation for users with multiple connections: fairness and stability publication-title: IEEE/ACM Trans. Netw. – reference: X. Ma, N. Elia, A distributed continuous-time gradient dynamics approach for the active power loss minimizations, in: Allerton Conf. on Communications, Control and Computing, Monticello, IL, 2013, pp. 100–106. – volume: 60 start-page: 443 year: 2012 end-page: 452 ident: br000020 article-title: Convergence analysis of saddle point problems in time varying wireless systems—control theoretical approach publication-title: IEEE Trans. Signal Process. – reference: X. Zhang, A. Papachristodoulou, Distributed dynamic feedback control for smart power networks with tree topology, in: American Control Conference, Portland, OR, 2014, pp. 1156–1161. – year: 2002 ident: br000050 article-title: Nonlinear Systems – volume: 59 start-page: 1177 year: 2014 end-page: 1189 ident: br000035 article-title: Design and stability of load-side primary frequency control in power systems publication-title: IEEE Trans. Automat. Control – volume: 42 start-page: 453 year: 2006 end-page: 458 ident: br000065 article-title: Nonpathological Lyapunov functions and discontinuous Caratheodory systems publication-title: Automatica – year: 1953 ident: br000075 article-title: Principles of Mathematical Analysis – volume: 46 start-page: 1974 year: 2010 ident: 10.1016/j.sysconle.2015.10.006_br000015 article-title: Stability of primal–dual gradient dynamics and applications to network optimization publication-title: Automatica doi: 10.1016/j.automatica.2010.08.011 – year: 2009 ident: 10.1016/j.sysconle.2015.10.006_br000085 – ident: 10.1016/j.sysconle.2015.10.006_br000030 doi: 10.1109/Allerton.2013.6736511 – year: 1953 ident: 10.1016/j.sysconle.2015.10.006_br000075 – volume: 22 start-page: 349 issue: 2 year: 2014 ident: 10.1016/j.sysconle.2015.10.006_br000025 article-title: Network resource allocation for users with multiple connections: fairness and stability publication-title: IEEE/ACM Trans. Netw. doi: 10.1109/TNET.2013.2251896 – volume: 59 start-page: 1177 issue: 5 year: 2014 ident: 10.1016/j.sysconle.2015.10.006_br000035 article-title: Design and stability of load-side primary frequency control in power systems publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2014.2298140 – volume: 17 start-page: 57 issue: 1 year: 2005 ident: 10.1016/j.sysconle.2015.10.006_br000090 article-title: The Krakovskii-LaSalle invariance principle for a class of unilateral dynamical systems publication-title: Math. Control Signals Syst. doi: 10.1007/s00498-004-0145-0 – volume: 42 start-page: 453 issue: 3 year: 2006 ident: 10.1016/j.sysconle.2015.10.006_br000065 article-title: Nonpathological Lyapunov functions and discontinuous Caratheodory systems publication-title: Automatica doi: 10.1016/j.automatica.2005.10.014 – volume: 60 start-page: 443 issue: 1 year: 2012 ident: 10.1016/j.sysconle.2015.10.006_br000020 article-title: Convergence analysis of saddle point problems in time varying wireless systems—control theoretical approach publication-title: IEEE Trans. Signal Process. doi: 10.1109/TSP.2011.2169407 – volume: 48 start-page: 2 issue: 1 year: 2003 ident: 10.1016/j.sysconle.2015.10.006_br000055 article-title: Dynamical properties of hybrid automata publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2002.806650 – year: 2002 ident: 10.1016/j.sysconle.2015.10.006_br000050 – volume: 22 start-page: 28 issue: 1 year: 2002 ident: 10.1016/j.sysconle.2015.10.006_br000100 article-title: Internet congestion control publication-title: IEEE Control Syst. Mag. doi: 10.1109/37.980245 – year: 1958 ident: 10.1016/j.sysconle.2015.10.006_br000005 – ident: 10.1016/j.sysconle.2015.10.006_br000045 doi: 10.1109/ACC.2014.6858966 – ident: 10.1016/j.sysconle.2015.10.006_br000040 doi: 10.1109/ALLERTON.2014.7028527 – volume: 24 start-page: 59 issue: 1 year: 1956 ident: 10.1016/j.sysconle.2015.10.006_br000010 article-title: Solutions of saddle value problems by differential equations publication-title: Econometrica doi: 10.2307/1905259 – year: 1983 ident: 10.1016/j.sysconle.2015.10.006_br000080 – volume: 49 start-page: 162 issue: 2 year: 2004 ident: 10.1016/j.sysconle.2015.10.006_br000095 article-title: A unifying passivity framework for network flow control publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2003.822858 – volume: 28 start-page: 36 issue: 3 year: 2008 ident: 10.1016/j.sysconle.2015.10.006_br000070 article-title: Discontinuous dynamical systems—a tutorial on solutions, nonsmooth analysis, and stability publication-title: IEEE Control Syst. Mag. – volume: vol.~2 year: 1996 ident: 10.1016/j.sysconle.2015.10.006_br000060 article-title: Projected dynamical systems and variational inequalities with applications |
| SSID | ssj0002033 |
| Score | 2.5565052 |
| Snippet | This paper studies the asymptotic convergence properties of the primal–dual dynamics designed for solving constrained concave optimization problems using... |
| SourceID | osti crossref elsevier |
| SourceType | Open Access Repository Enrichment Source Index Database Publisher |
| StartPage | 10 |
| SubjectTerms | Caratheodory solutions Constrained optimization Discontinuous dynamics Primal–dual dynamics Saddle points |
| Title | Asymptotic convergence of constrained primal–dual dynamics |
| URI | https://dx.doi.org/10.1016/j.sysconle.2015.10.006 https://www.osti.gov/biblio/1556180 |
| Volume | 87 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV29TsMwELaqssCA-BWlUGVgTZMmtpNKLFVFVajoAEV0ixzbkVqVJmrC0AXxDrwhT8JdfqAMqANTZMsXWWff-Wx99x0hVzYPuy5X1ARroCbtRBGYlOAmDeFuACeWqxUmON-P-fCJ3k3ZtEb6VS4MwipL31_49Nxblz1WqU0rmc2sRwTQc7RVhjGPhwm_lHq4y9tvPzAPxy7KySO_N47eyBKet9N1CrfOBdJldli7QHn9dUDVY7C5jbNncED2y6DR6BXzOiQ1vTwiextUgsfkupeuX5IshhFGjiTPkyq1EUfYTPNKEFoZCZJLLD7fPzAFy1BFOfr0hEwGN5P-0CwrI5iSMjczlfJtTcEamdaSCscFtTIluJAa-f9cWBnGHKUdHQkhbV9DHBH5cNNAVKeQ7impL-OlPiOGzYTthZ70JNVUIv8bV5wr5QjV5SGlDcIqbQSyZA3HKS-CCh42DyotBqhF7ActNoj1LZcUvBlbJbqVsoNfOyAA575Vtomrg3JIfSsRIwSCHaz96dvn__hzk-xCq3x0uSD1bPWqLyEMycJWvs9aZKd3OxqO8Tt6eB59Ac-94Cw |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwELZKGYAB8RSlPDKwpkkT20kllqoCFWi7UKRukWM7UqvSRCQMXRD_gX_IL-EuDygD6sAYxxc5Z9_5bH33HSFXNg87LlfUBGugJm1HEZiU4CYN4WwAO5arFSY4D0e8_0TvJ2xSI70qFwZhlaXvL3x67q3LFqvUppVMp9YjAug52irDmMfzN8gmBfPFMgattx-ch2MX9eSR4Bu7r6QJz1rpMoVj5xz5MtusVcC8_tqh6jEY3crmc7tHdsuo0egWA9snNb04IDsrXIKH5LqbLp-TLIYeRg4lz7MqtRFH-JjmpSC0MhJkl5h_vn9gDpahinr06REZ396Me32zLI1gSvjHzFTKtzUFc2RaSyocF_TKlOBCaiQAdGFqGHOUdnQkhLR9DYFE5MNRA2GdQrrHpL6IF_qEGDYTthd60pNUU4kEcFxxrpQjVIeHlDYIq7QRyJI2HIc8Dyp82CyotBigFrEdtNgg1rdcUhBnrJXoVMoOfi2BALz7Wtkmzg7KIfetRJAQCLax-Kdvn_7jy5dkqz8eDoLB3eihSbbhTXkDc0bq2curPoeYJAsv8jX3BQUf4Bc |
| 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=Asymptotic+convergence+of+constrained+primal%E2%80%93dual+dynamics&rft.jtitle=Systems+%26+control+letters&rft.au=Cherukuri%2C+Ashish&rft.au=Mallada%2C+Enrique&rft.au=Cort%C3%A9s%2C+Jorge&rft.date=2016-01-01&rft.issn=0167-6911&rft.volume=87&rft.spage=10&rft.epage=15&rft_id=info:doi/10.1016%2Fj.sysconle.2015.10.006&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_sysconle_2015_10_006 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-6911&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-6911&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-6911&client=summon |