A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity
In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum ter...
Saved in:
| Published in: | Journal of computational and applied mathematics Vol. 422; p. 114919 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.04.2023
|
| Subjects: | |
| ISSN: | 0377-0427, 1879-1778 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum term to minimize the objective functional containing random terms. A full error analysis including Monte Carlo, finite element, and stochastic momentum gradient iteration errors is done. Numerical examples are presented to illustrate the performance of the proposed stochastic approximations in the PDE-constrained optimization setting. |
|---|---|
| AbstractList | In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with uncertain terms. Our approach is based on stochastic approximation where true gradient is replaced by a stochastic ones with suitable momentum term to minimize the objective functional containing random terms. A full error analysis including Monte Carlo, finite element, and stochastic momentum gradient iteration errors is done. Numerical examples are presented to illustrate the performance of the proposed stochastic approximations in the PDE-constrained optimization setting. |
| ArticleNumber | 114919 |
| Author | Toraman, Sıtkı Can Yücel, Hamdullah |
| Author_xml | – sequence: 1 givenname: Sıtkı Can orcidid: 0000-0002-1623-4050 surname: Toraman fullname: Toraman, Sıtkı Can email: storaman@metu.edu.tr – sequence: 2 givenname: Hamdullah surname: Yücel fullname: Yücel, Hamdullah email: yucelh@metu.edu.tr |
| BookMark | eNp9kM1KAzEUhYNUsK0-gLu8wNQkE80MrqT4B4IbXYdMclNTZiY1SSvd-Q6CD-iTmLFduejm3ss5nAvnm6BR73tA6JySGSX06mI506qbMcLYjFJe0_oIjWkl6oIKUY3QmJRCFIQzcYImMS4JIVc15WP0fYNj8vpNxeQ0XgRlHPQJq3bhg0tvHf7IE3e-y-q6wwlCF7H1AftVcp1qsfZ9Cr7Fq-CbFrK58BsIPRjcbLEa7A3o5Hz_8_llnLXrmG8M72s1iLv3QfXGd3hvb1zanqJjq9oIZ_s9Ra93ty_zh-Lp-f5xfvNUaMZEKqrSqhIaaJpLVnEOQChjmtcVN5rYkhmluaaKG0FLkvtCySgTwl6yLFBhyymiu786-BgDWLkKuVbYSkrkAFYuZQYrB7ByBzZnxL-MdumvTQrKtQeT17sk5EobB0FGnXFrMC5kSNJ4dyD9CwOjmlQ |
| CitedBy_id | crossref_primary_10_1007_s10489_023_05249_1 crossref_primary_10_1016_j_jmaa_2023_127634 crossref_primary_10_1016_j_energy_2023_129139 crossref_primary_10_1088_1751_8121_ad4b7c crossref_primary_10_1080_02331934_2025_2541709 crossref_primary_10_1016_j_tsep_2025_104083 |
| Cites_doi | 10.1007/s10589-020-00220-z 10.1137/18M1200208 10.1137/11081126X 10.1137/16M1080173 10.1016/j.camwa.2014.12.010 10.1137/070711311 10.1137/16M1057607 10.1137/19M1294952 10.1137/19M125902X 10.1214/aoms/1177729392 10.1137/S0036142902418680 10.1561/2200000050 10.1016/j.jcp.2011.01.023 10.1016/j.crma.2014.04.007 10.1137/110835438 10.1016/j.automatica.2014.10.054 10.1093/imanum/drn014 10.1007/s00791-010-0134-4 10.1137/S1064827592240555 10.1051/m2an/2021025 10.1137/070704277 10.1016/j.cma.2011.11.026 10.1137/100801731 10.1016/S0045-7825(02)00354-7 10.1137/17M1155892 10.1016/0041-5553(64)90137-5 10.1137/120884158 10.1137/15M1041390 10.1137/19M1263297 10.1002/gamm.201010017 10.1137/16M109870X 10.1214/aoms/1177729586 10.1016/j.jmaa.2010.07.036 10.1137/120892362 10.1137/15M1018502 |
| ContentType | Journal Article |
| Copyright | 2022 Elsevier B.V. |
| Copyright_xml | – notice: 2022 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.cam.2022.114919 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1879-1778 |
| ExternalDocumentID | 10_1016_j_cam_2022_114919 S0377042722005179 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAFWJ AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 D-I DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HVGLF HZ~ IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NCXOZ NHB O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 UPT WUQ XPP YQT ZMT ZY4 ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD |
| ID | FETCH-LOGICAL-c227t-83fa3ebebb52844ee0122c4984dc0f32dac4c1a4d7130914e321277f5271317f3 |
| ISICitedReferencesCount | 7 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000993124300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0377-0427 |
| IngestDate | Tue Nov 18 21:33:56 EST 2025 Sat Nov 29 07:22:16 EST 2025 Fri Feb 23 02:38:41 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | 35R60 49J20 Monte Carlo PDE-constrained optimization Stochastic momentum Uncertainty quantification 65C05 60H15 60H35 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c227t-83fa3ebebb52844ee0122c4984dc0f32dac4c1a4d7130914e321277f5271317f3 |
| ORCID | 0000-0002-1623-4050 |
| ParticipantIDs | crossref_primary_10_1016_j_cam_2022_114919 crossref_citationtrail_10_1016_j_cam_2022_114919 elsevier_sciencedirect_doi_10_1016_j_cam_2022_114919 |
| PublicationCentury | 2000 |
| PublicationDate | April 2023 2023-04-00 |
| PublicationDateYYYYMMDD | 2023-04-01 |
| PublicationDate_xml | – month: 04 year: 2023 text: April 2023 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of computational and applied mathematics |
| PublicationYear | 2023 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Loizou, Richtárik (b47) 2020; 77 Benner, Onwunta, Stoll (b15) 2016; 37 Chen, Quarteroni, Rozza (b16) 2013; 51 Robbins, Monro (b23) 1951; 22 Bottou, Curtis, Nocedal (b24) 2018; 60 Geiersbach, Pflug (b26) 2019; 29 M. Martin, F. Nobile, P. Tsilifis, A Multilevel Stochastic Gradient Method for PDE–Constrained Optimal Control Problems with Uncertain Parameters, Tech. rep., 2019 Polyak (b32) 1964; 4 Lee, Lee (b13) 2013; 14 Kiefer, Wolfowitz (b22) 1952; 30 Martin, Krumscheid, Nobile (b28) 2021; 55 Haber, Chung, Herrmann (b25) 2012; 22 Kunoth, Schwab (b17) 2016; 4 Babuška, Chatzipantelidis (b40) 2002; 191 Garreis, Ulbrich (b9) 2017; 39 Nesterov (b33) 1983; 27 Assran, Rabbat (b48) 2020 P. Çiloğlu, H. Yücel, Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients, Tech. rep., 2021 Karhunen (b38) 1947 . Tröltzsch (b37) 2010 Rosseel, Wells (b14) 2012; 213/216 Babuška, Tempone, Zouraris (b34) 2004; 42 Dietrich, Newsam (b43) 1997; 18 Zuazua (b5) 2014; 50 Guth, Kaarnioja, Kuo, Schillings, Sloan (b20) 2021; 9 Nemirovski, Juditsky, Lan, Shapiro (b31) 2009; 19 Brenner, Scott (b45) 2002 Geiersbach, Wollner (b27) 2020; 42 Graham, Kuo, Nuyens, Scheichl, Sloan (b44) 2011; 230 Barel, Vandewalle (b21) 2019; 7 Hou, Lee, Manouzi (b11) 2011; 384 Gunzburger, Lee, Lee (b10) 2011; 49 Borzì, von Winckel (b19) 2009; 31 Tiesler, Kirby, Xiu, Preusser (b18) 2012; 50 Roache (b1) 1998 Kouri, Heinkenschloss, Ridzal, van Bloemen Waanders (b12) 2013; 35 Ali, Ullmann, Hinze (b3) 2017; 5 Loève (b39) 1946; 84 Borzì (b6) 2010; 13 Wanga, Knap (b30) 2021; 426 Lazar, Zuazua (b4) 2014; 352 Borzì, Schulz, Schillings, von Winckel (b7) 2010; 33 Lions (b36) 1971 Powell, Elman (b42) 2009; 29 Lord, Powell, Shardlow (b35) 2014 Kubinova, Pultarova (b41) 2020; 8 Negri, Manzoni, Rozza (b2) 2015; 69 Bubeck (b46) 2015; 8 Loève (10.1016/j.cam.2022.114919_b39) 1946; 84 Kubinova (10.1016/j.cam.2022.114919_b41) 2020; 8 Kunoth (10.1016/j.cam.2022.114919_b17) 2016; 4 Tiesler (10.1016/j.cam.2022.114919_b18) 2012; 50 Kiefer (10.1016/j.cam.2022.114919_b22) 1952; 30 Babuška (10.1016/j.cam.2022.114919_b34) 2004; 42 Bottou (10.1016/j.cam.2022.114919_b24) 2018; 60 Garreis (10.1016/j.cam.2022.114919_b9) 2017; 39 Chen (10.1016/j.cam.2022.114919_b16) 2013; 51 Robbins (10.1016/j.cam.2022.114919_b23) 1951; 22 Barel (10.1016/j.cam.2022.114919_b21) 2019; 7 Benner (10.1016/j.cam.2022.114919_b15) 2016; 37 Kouri (10.1016/j.cam.2022.114919_b12) 2013; 35 Borzì (10.1016/j.cam.2022.114919_b7) 2010; 33 Nemirovski (10.1016/j.cam.2022.114919_b31) 2009; 19 Gunzburger (10.1016/j.cam.2022.114919_b10) 2011; 49 Borzì (10.1016/j.cam.2022.114919_b19) 2009; 31 Polyak (10.1016/j.cam.2022.114919_b32) 1964; 4 Guth (10.1016/j.cam.2022.114919_b20) 2021; 9 Karhunen (10.1016/j.cam.2022.114919_b38) 1947 Dietrich (10.1016/j.cam.2022.114919_b43) 1997; 18 10.1016/j.cam.2022.114919_b29 Lord (10.1016/j.cam.2022.114919_b35) 2014 Borzì (10.1016/j.cam.2022.114919_b6) 2010; 13 Geiersbach (10.1016/j.cam.2022.114919_b26) 2019; 29 Nesterov (10.1016/j.cam.2022.114919_b33) 1983; 27 Martin (10.1016/j.cam.2022.114919_b28) 2021; 55 Babuška (10.1016/j.cam.2022.114919_b40) 2002; 191 Wanga (10.1016/j.cam.2022.114919_b30) 2021; 426 Tröltzsch (10.1016/j.cam.2022.114919_b37) 2010 Geiersbach (10.1016/j.cam.2022.114919_b27) 2020; 42 Hou (10.1016/j.cam.2022.114919_b11) 2011; 384 Brenner (10.1016/j.cam.2022.114919_b45) 2002 Zuazua (10.1016/j.cam.2022.114919_b5) 2014; 50 Powell (10.1016/j.cam.2022.114919_b42) 2009; 29 Graham (10.1016/j.cam.2022.114919_b44) 2011; 230 Bubeck (10.1016/j.cam.2022.114919_b46) 2015; 8 Loizou (10.1016/j.cam.2022.114919_b47) 2020; 77 Ali (10.1016/j.cam.2022.114919_b3) 2017; 5 10.1016/j.cam.2022.114919_b8 Lions (10.1016/j.cam.2022.114919_b36) 1971 Roache (10.1016/j.cam.2022.114919_b1) 1998 Negri (10.1016/j.cam.2022.114919_b2) 2015; 69 Rosseel (10.1016/j.cam.2022.114919_b14) 2012; 213/216 Assran (10.1016/j.cam.2022.114919_b48) 2020 Lee (10.1016/j.cam.2022.114919_b13) 2013; 14 Lazar (10.1016/j.cam.2022.114919_b4) 2014; 352 Haber (10.1016/j.cam.2022.114919_b25) 2012; 22 |
| References_xml | – volume: 77 start-page: 653 year: 2020 end-page: 710 ident: b47 article-title: Momentum and stochastic momentum for stochastic gradient, Newton, proximal point and subspace descent methods publication-title: Comput. Optim. Appl. – volume: 213/216 start-page: 152 year: 2012 end-page: 167 ident: b14 article-title: Optimal control with stochastic PDE constraints and uncertain controls publication-title: Comput. Methods Appl. Mech. Eng. – volume: 29 start-page: 350 year: 2009 end-page: 375 ident: b42 article-title: Block–diagonal preconditioning for spectral stochastic finite–element systems publication-title: IMA J. Numer. Anal. – year: 1971 ident: b36 article-title: Optimal Control of Systems Governed by Partial Differential Equations – year: 2010 ident: b37 publication-title: Optimal Control of Partial Differential Equations: Theory, Methods and Applications – volume: 37 start-page: 491 year: 2016 end-page: 518 ident: b15 article-title: Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs publication-title: SIAM. J. Matrix Anal. & Appl. – volume: 22 start-page: 400 year: 1951 end-page: 407 ident: b23 article-title: A stochastic approximation method publication-title: Ann. Math. Stat. – volume: 8 start-page: 231 year: 2015 end-page: 357 ident: b46 article-title: Convex optimization: Algorithms and complexity publication-title: Found. Trends Mach. Learn. – volume: 191 start-page: 4093 year: 2002 end-page: 4122 ident: b40 article-title: On solving elliptic stochastic partial differential equations publication-title: Comput. Methods Appl. Mech. Engrg. – volume: 13 start-page: 153 year: 2010 end-page: 160 ident: b6 article-title: Multigrid and sparse-grid schemes for elliptic control problems with random coefficients publication-title: Comput. Vis. Sci. – volume: 42 start-page: A2750 year: 2020 end-page: A2772 ident: b27 article-title: A stochastic gradient method with mesh refinement for PDE–constrained optimization under uncertainity publication-title: SIAM J. Sci. Comput. – volume: 230 start-page: 3668 year: 2011 end-page: 3694 ident: b44 article-title: Quasi–Monte Carlo methods for elliptic PDEs with random coefficients and applications publication-title: J. Comput. Phys. – volume: 31 start-page: 2172 year: 2009 end-page: 2192 ident: b19 article-title: Multigrid methods and sparse-grid collocation techniques for parabolic optimal control problems with random coefficients publication-title: SIAM J. Sci. Comput. – reference: P. Çiloğlu, H. Yücel, Stochastic Discontinuous Galerkin Methods for Robust Deterministic Control of Convection Diffusion Equations with Uncertain Coefficients, Tech. rep., 2021, – year: 1998 ident: b1 article-title: Verification & Validation in Computational Science and Engineering – volume: 27 start-page: 372 year: 1983 end-page: 376 ident: b33 article-title: A method for solving a convex programming problem with convergence rate publication-title: Soviet Math. Dokl. – reference: M. Martin, F. Nobile, P. Tsilifis, A Multilevel Stochastic Gradient Method for PDE–Constrained Optimal Control Problems with Uncertain Parameters, Tech. rep., 2019, – volume: 4 start-page: 1 year: 1964 end-page: 17 ident: b32 article-title: Some methods of speeding up the convergence of iteration methods publication-title: USSR Comput. Math. & Math. Phys. – volume: 49 start-page: 1532 year: 2011 end-page: 1552 ident: b10 article-title: Error estimates of stochastic optimal Neumann boundary control problems publication-title: SIAM J. Numer. Anal. – volume: 426 year: 2021 ident: b30 article-title: Stochastic gradient descent for semilinear elliptic equations with uncertainties publication-title: J. Comput. Phys. – volume: 50 start-page: 3077 year: 2014 end-page: 3087 ident: b5 article-title: Averaged control publication-title: Automatica – volume: 352 start-page: 497 year: 2014 end-page: 502 ident: b4 article-title: Averaged control and observation of parameter-depending wave equations publication-title: C. R. Math. Acad. Sci. Paris – volume: 22 start-page: 739 year: 2012 end-page: 757 ident: b25 article-title: An effective method for parameter estimation with PDE constraints with multiple right–hand side publication-title: SIAM J. Optim. – volume: 9 start-page: 354 year: 2021 end-page: 383 ident: b20 article-title: A quasi-Monte Carlo method for optimal control under uncertainty publication-title: SIAM/ASA J. Uncertain. Quantif. – volume: 39 start-page: A25 year: 2017 end-page: A54 ident: b9 article-title: Constrained optimization with low-rank tensors and applications to parametric problems with PDEs publication-title: SIAM J. Sci. Comput. – year: 2014 ident: b35 article-title: An Introduction to Computational Stochastic PDEs – volume: 8 start-page: 88 year: 2020 end-page: 113 ident: b41 article-title: Block preconditioning of stochastic Galerkin problems: New two-sided guaranteed spectral bounds publication-title: SIAM/ASA J. Uncertain. Quantif. – volume: 50 start-page: 2659 year: 2012 end-page: 2682 ident: b18 article-title: Stochastic collocation for optimal control problems with stochastic PDE constraints publication-title: SIAM J. Control Optim. – start-page: 410 year: 2020 end-page: 420 ident: b48 article-title: On the convergence of Nesterov’s accelerated gradient method in stochastic settings publication-title: Proceedings of the 37th International Conference on Machine Learning – volume: 33 start-page: 230 year: 2010 end-page: 246 ident: b7 article-title: On the treatment of distributed uncertainties in PDE constrained optimization publication-title: GAMM-Mitt. – volume: 5 start-page: 466 year: 2017 end-page: 492 ident: b3 article-title: Multilevel Monte Carlo analysis for optimal control of elliptic PDEs with random coefficients publication-title: SIAM/ASA J. Uncertain. Quantif. – volume: 60 start-page: 223 year: 2018 end-page: 311 ident: b24 article-title: Optimization methods for large-scale machine learning publication-title: SIAM Rev. – volume: 7 start-page: 174 year: 2019 end-page: 202 ident: b21 article-title: Robust optimization of PDEs with random coefficients using a multilevel Monte Carlo method publication-title: SIAM/ASA J. Uncertain. Quantif. – volume: 35 start-page: A1847 year: 2013 end-page: A1879 ident: b12 article-title: A trust-region algorithm with adaptive stochastic collocation for PDE optimization under uncertainty publication-title: SIAM J. Sci. Comput. – volume: 4 start-page: 1034 year: 2016 end-page: 1059 ident: b17 article-title: Sparse adaptive tensor Galerkin approximations of stochastic PDE-constrained control problems publication-title: SIAM/ASA J. Uncertain. Quantif. – volume: 14 start-page: 77 year: 2013 end-page: 106 ident: b13 article-title: A stochastic Galerkin method for stochastic control problems publication-title: Commun. Comput. Phys. – volume: 30 start-page: 462 year: 1952 end-page: 466 ident: b22 article-title: Stochastic estimation of the maximum of a regression function publication-title: Ann. Math. Stat. – volume: 51 start-page: 2700 year: 2013 end-page: 2722 ident: b16 article-title: Stochastic optimal robin boundary control problems of advection-dominated elliptic equations publication-title: SIAM J. Numer. Anal. – volume: 84 start-page: 195 year: 1946 end-page: 206 ident: b39 article-title: Fonctions aléatoires de second ordre publication-title: Revue Sci. – reference: . – volume: 19 start-page: 1574 year: 2009 end-page: 1609 ident: b31 article-title: Robust stochastic approximation approach to stochastic programming publication-title: SIAM J. Optim. – start-page: 79 year: 1947 ident: b38 article-title: Über Lineare Methoden in der Wahrscheinlichkeitsrechnung publication-title: Ann. Acad. Sci. Fenn. Ser. A. I. Math.-Phys. – volume: 18 start-page: 1088 year: 1997 end-page: 1107 ident: b43 article-title: Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix publication-title: SIAM J. Sci. Comput. – volume: 42 start-page: 800 year: 2004 end-page: 825 ident: b34 article-title: Galerkin finite element approximations of stochastic elliptic partial differential equations publication-title: SIAM J. Numer. Anal. – year: 2002 ident: b45 article-title: The Mathematical Theory of Finite Element Methods – volume: 384 start-page: 87 year: 2011 end-page: 103 ident: b11 article-title: Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs publication-title: J. Math. Anal. Appl. – volume: 69 start-page: 319 year: 2015 end-page: 336 ident: b2 article-title: Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations publication-title: Comput. Math. Appl. – volume: 29 start-page: 2079 year: 2019 end-page: 2099 ident: b26 article-title: Projected stochastic gradients for convex constrained problems in Hilbert spaces publication-title: SIAM J. Optim. – volume: 55 start-page: 1599 year: 2021 end-page: 1633 ident: b28 article-title: Complexity analysis of stochastic gradient methods for PDE–constrained optimal control problems with uncertain parameters publication-title: ESAIM Math. Model. Numer. Anal. – volume: 77 start-page: 653 issue: 3 year: 2020 ident: 10.1016/j.cam.2022.114919_b47 article-title: Momentum and stochastic momentum for stochastic gradient, Newton, proximal point and subspace descent methods publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-020-00220-z – volume: 14 start-page: 77 year: 2013 ident: 10.1016/j.cam.2022.114919_b13 article-title: A stochastic Galerkin method for stochastic control problems publication-title: Commun. Comput. Phys. – volume: 29 start-page: 2079 year: 2019 ident: 10.1016/j.cam.2022.114919_b26 article-title: Projected stochastic gradients for convex constrained problems in Hilbert spaces publication-title: SIAM J. Optim. doi: 10.1137/18M1200208 – year: 2014 ident: 10.1016/j.cam.2022.114919_b35 – year: 2002 ident: 10.1016/j.cam.2022.114919_b45 – volume: 22 start-page: 739 year: 2012 ident: 10.1016/j.cam.2022.114919_b25 article-title: An effective method for parameter estimation with PDE constraints with multiple right–hand side publication-title: SIAM J. Optim. doi: 10.1137/11081126X – volume: 60 start-page: 223 issue: 2 year: 2018 ident: 10.1016/j.cam.2022.114919_b24 article-title: Optimization methods for large-scale machine learning publication-title: SIAM Rev. doi: 10.1137/16M1080173 – volume: 69 start-page: 319 issue: 4 year: 2015 ident: 10.1016/j.cam.2022.114919_b2 article-title: Reduced basis approximation of parametrized optimal flow control problems for the Stokes equations publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2014.12.010 – volume: 31 start-page: 2172 issue: 3 year: 2009 ident: 10.1016/j.cam.2022.114919_b19 article-title: Multigrid methods and sparse-grid collocation techniques for parabolic optimal control problems with random coefficients publication-title: SIAM J. Sci. Comput. doi: 10.1137/070711311 – volume: 39 start-page: A25 year: 2017 ident: 10.1016/j.cam.2022.114919_b9 article-title: Constrained optimization with low-rank tensors and applications to parametric problems with PDEs publication-title: SIAM J. Sci. Comput. doi: 10.1137/16M1057607 – volume: 9 start-page: 354 issue: 2 year: 2021 ident: 10.1016/j.cam.2022.114919_b20 article-title: A quasi-Monte Carlo method for optimal control under uncertainty publication-title: SIAM/ASA J. Uncertain. Quantif. doi: 10.1137/19M1294952 – volume: 8 start-page: 88 issue: 1 year: 2020 ident: 10.1016/j.cam.2022.114919_b41 article-title: Block preconditioning of stochastic Galerkin problems: New two-sided guaranteed spectral bounds publication-title: SIAM/ASA J. Uncertain. Quantif. doi: 10.1137/19M125902X – volume: 30 start-page: 462 year: 1952 ident: 10.1016/j.cam.2022.114919_b22 article-title: Stochastic estimation of the maximum of a regression function publication-title: Ann. Math. Stat. doi: 10.1214/aoms/1177729392 – start-page: 410 year: 2020 ident: 10.1016/j.cam.2022.114919_b48 article-title: On the convergence of Nesterov’s accelerated gradient method in stochastic settings – volume: 42 start-page: 800 issue: 2 year: 2004 ident: 10.1016/j.cam.2022.114919_b34 article-title: Galerkin finite element approximations of stochastic elliptic partial differential equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142902418680 – volume: 8 start-page: 231 issue: 3–4 year: 2015 ident: 10.1016/j.cam.2022.114919_b46 article-title: Convex optimization: Algorithms and complexity publication-title: Found. Trends Mach. Learn. doi: 10.1561/2200000050 – volume: 230 start-page: 3668 year: 2011 ident: 10.1016/j.cam.2022.114919_b44 article-title: Quasi–Monte Carlo methods for elliptic PDEs with random coefficients and applications publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2011.01.023 – volume: 352 start-page: 497 year: 2014 ident: 10.1016/j.cam.2022.114919_b4 article-title: Averaged control and observation of parameter-depending wave equations publication-title: C. R. Math. Acad. Sci. Paris doi: 10.1016/j.crma.2014.04.007 – volume: 50 start-page: 2659 issue: 5 year: 2012 ident: 10.1016/j.cam.2022.114919_b18 article-title: Stochastic collocation for optimal control problems with stochastic PDE constraints publication-title: SIAM J. Control Optim. doi: 10.1137/110835438 – volume: 50 start-page: 3077 issue: 12 year: 2014 ident: 10.1016/j.cam.2022.114919_b5 article-title: Averaged control publication-title: Automatica doi: 10.1016/j.automatica.2014.10.054 – volume: 29 start-page: 350 issue: 2 year: 2009 ident: 10.1016/j.cam.2022.114919_b42 article-title: Block–diagonal preconditioning for spectral stochastic finite–element systems publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drn014 – volume: 426 year: 2021 ident: 10.1016/j.cam.2022.114919_b30 article-title: Stochastic gradient descent for semilinear elliptic equations with uncertainties publication-title: J. Comput. Phys. – year: 1971 ident: 10.1016/j.cam.2022.114919_b36 – volume: 13 start-page: 153 year: 2010 ident: 10.1016/j.cam.2022.114919_b6 article-title: Multigrid and sparse-grid schemes for elliptic control problems with random coefficients publication-title: Comput. Vis. Sci. doi: 10.1007/s00791-010-0134-4 – year: 2010 ident: 10.1016/j.cam.2022.114919_b37 – start-page: 79 issue: 37 year: 1947 ident: 10.1016/j.cam.2022.114919_b38 article-title: Über Lineare Methoden in der Wahrscheinlichkeitsrechnung publication-title: Ann. Acad. Sci. Fenn. Ser. A. I. Math.-Phys. – volume: 18 start-page: 1088 year: 1997 ident: 10.1016/j.cam.2022.114919_b43 article-title: Fast and exact simulation of stationary Gaussian processes through circulant embedding of the covariance matrix publication-title: SIAM J. Sci. Comput. doi: 10.1137/S1064827592240555 – volume: 55 start-page: 1599 issue: 4 year: 2021 ident: 10.1016/j.cam.2022.114919_b28 article-title: Complexity analysis of stochastic gradient methods for PDE–constrained optimal control problems with uncertain parameters publication-title: ESAIM Math. Model. Numer. Anal. doi: 10.1051/m2an/2021025 – volume: 19 start-page: 1574 issue: 4 year: 2009 ident: 10.1016/j.cam.2022.114919_b31 article-title: Robust stochastic approximation approach to stochastic programming publication-title: SIAM J. Optim. doi: 10.1137/070704277 – volume: 213/216 start-page: 152 year: 2012 ident: 10.1016/j.cam.2022.114919_b14 article-title: Optimal control with stochastic PDE constraints and uncertain controls publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2011.11.026 – volume: 49 start-page: 1532 issue: 4 year: 2011 ident: 10.1016/j.cam.2022.114919_b10 article-title: Error estimates of stochastic optimal Neumann boundary control problems publication-title: SIAM J. Numer. Anal. doi: 10.1137/100801731 – volume: 84 start-page: 195 year: 1946 ident: 10.1016/j.cam.2022.114919_b39 article-title: Fonctions aléatoires de second ordre publication-title: Revue Sci. – volume: 191 start-page: 4093 issue: 37–38 year: 2002 ident: 10.1016/j.cam.2022.114919_b40 article-title: On solving elliptic stochastic partial differential equations publication-title: Comput. Methods Appl. Mech. Engrg. doi: 10.1016/S0045-7825(02)00354-7 – volume: 7 start-page: 174 issue: 1 year: 2019 ident: 10.1016/j.cam.2022.114919_b21 article-title: Robust optimization of PDEs with random coefficients using a multilevel Monte Carlo method publication-title: SIAM/ASA J. Uncertain. Quantif. doi: 10.1137/17M1155892 – ident: 10.1016/j.cam.2022.114919_b29 – volume: 4 start-page: 1 issue: 5 year: 1964 ident: 10.1016/j.cam.2022.114919_b32 article-title: Some methods of speeding up the convergence of iteration methods publication-title: USSR Comput. Math. & Math. Phys. doi: 10.1016/0041-5553(64)90137-5 – year: 1998 ident: 10.1016/j.cam.2022.114919_b1 – volume: 51 start-page: 2700 year: 2013 ident: 10.1016/j.cam.2022.114919_b16 article-title: Stochastic optimal robin boundary control problems of advection-dominated elliptic equations publication-title: SIAM J. Numer. Anal. doi: 10.1137/120884158 – volume: 4 start-page: 1034 year: 2016 ident: 10.1016/j.cam.2022.114919_b17 article-title: Sparse adaptive tensor Galerkin approximations of stochastic PDE-constrained control problems publication-title: SIAM/ASA J. Uncertain. Quantif. doi: 10.1137/15M1041390 – volume: 42 start-page: A2750 issue: 5 year: 2020 ident: 10.1016/j.cam.2022.114919_b27 article-title: A stochastic gradient method with mesh refinement for PDE–constrained optimization under uncertainity publication-title: SIAM J. Sci. Comput. doi: 10.1137/19M1263297 – volume: 27 start-page: 372 year: 1983 ident: 10.1016/j.cam.2022.114919_b33 article-title: A method for solving a convex programming problem with convergence rate O(1/k2) publication-title: Soviet Math. Dokl. – volume: 33 start-page: 230 issue: 2 year: 2010 ident: 10.1016/j.cam.2022.114919_b7 article-title: On the treatment of distributed uncertainties in PDE constrained optimization publication-title: GAMM-Mitt. doi: 10.1002/gamm.201010017 – volume: 5 start-page: 466 year: 2017 ident: 10.1016/j.cam.2022.114919_b3 article-title: Multilevel Monte Carlo analysis for optimal control of elliptic PDEs with random coefficients publication-title: SIAM/ASA J. Uncertain. Quantif. doi: 10.1137/16M109870X – ident: 10.1016/j.cam.2022.114919_b8 – volume: 22 start-page: 400 year: 1951 ident: 10.1016/j.cam.2022.114919_b23 article-title: A stochastic approximation method publication-title: Ann. Math. Stat. doi: 10.1214/aoms/1177729586 – volume: 384 start-page: 87 year: 2011 ident: 10.1016/j.cam.2022.114919_b11 article-title: Finite element approximations of stochastic optimal control problems constrained by stochastic elliptic PDEs publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2010.07.036 – volume: 35 start-page: A1847 year: 2013 ident: 10.1016/j.cam.2022.114919_b12 article-title: A trust-region algorithm with adaptive stochastic collocation for PDE optimization under uncertainty publication-title: SIAM J. Sci. Comput. doi: 10.1137/120892362 – volume: 37 start-page: 491 year: 2016 ident: 10.1016/j.cam.2022.114919_b15 article-title: Block-diagonal preconditioning for optimal control problems constrained by PDEs with uncertain inputs publication-title: SIAM. J. Matrix Anal. & Appl. doi: 10.1137/15M1018502 |
| SSID | ssj0006914 |
| Score | 2.4172873 |
| Snippet | In this paper, we focus on a numerical investigation of a strongly convex and smooth optimization problem subject to a convection–diffusion equation with... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 114919 |
| SubjectTerms | Monte Carlo PDE-constrained optimization Stochastic momentum Uncertainty quantification |
| Title | A stochastic gradient algorithm with momentum terms for optimal control problems governed by a convection–diffusion equation with random diffusivity |
| URI | https://dx.doi.org/10.1016/j.cam.2022.114919 |
| Volume | 422 |
| WOSCitedRecordID | wos000993124300001&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: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1879-1778 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: AIEXJ dateStart: 20211207 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3LbtQwFLWGlgUsEE9RCsgLVkRBjePU8XI6KioIKhaDNKwix7Gnr2TKNFO1O_4BiV_hf_gSrl_JUBhEF2wykSdxotyT6-Ob63MReiGoqmBYlHGudRZToin4wbyKpTLlj0SqubIiru_Y_n4-mfAPg8H3sBbm_IQ1TX5xwU__q6mhDYxtls5ew9xdp9AA-2B02ILZYftPhh9GwOfkgTACzNF0blO6TFx3Opsftge1i7zWRnihXdSR8cxWkiGagfOorVqIS173pWbOoqktx-uYqnBp6nYxRMiTSE2RlYWJukXqs1MOdxeBYbCa1ZH_2xSpWEGFpS0tEcKSVj7Wk-O6U5XtuP8YQBvCtoYK7yTtsfuNRj3UP5kMgJ2RdEkIe6KuYK7tY98-yEHSpdwYv7iLsdiUBVl23NStaPauFyZ23Hnf30YFF6A4ghm_0R4g5FV_7K8K3FdGxi5fMaTCHRXQRWG6KFwXN9A6YRkHd7o-fLM7eduRgG3uZOXDfYcP6ja18Mp9_JkSLdGc8V10xxsFDx2u7qGBau6j2-97MzxA34a4RxgOCMMdwrAxPg4IwxZhGBCGPcKwRxgOCMMBYbi8xAL3CPvx5WuHLRyw5bp32MJL2HqIPr7eHY_2Yl_eI5aEsDbOUy1S8CFlmQFHokqZr7yS8pxWckunpBKSykTQigHPgsepUlONgOmMQEPCdPoIrTWzRj1GOEt1UuaZqDSTlJbbPM8Iz5NMZiIhipMNtBWecCG99r0pwXJSrLTsBnrZnXLqhF_-djANZis8c3WMtAAIrj7tyXWusYlu9W_GU7TWzhfqGbopz9vDs_lzj7-fUpDAIw |
| linkProvider | Elsevier |
| 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=A+stochastic+gradient+algorithm+with+momentum+terms+for+optimal+control+problems+governed+by+a+convection%E2%80%93diffusion+equation+with+random+diffusivity&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Toraman%2C+S%C4%B1tk%C4%B1+Can&rft.au=Y%C3%BCcel%2C+Hamdullah&rft.date=2023-04-01&rft.issn=0377-0427&rft.volume=422&rft.spage=114919&rft_id=info:doi/10.1016%2Fj.cam.2022.114919&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cam_2022_114919 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon |