Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method
In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method. In particular, we consider the framework o...
Saved in:
| Published in: | Journal of computational physics Vol. 495; p. 112523 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Inc
15.12.2023
|
| Subjects: | |
| ISSN: | 0021-9991, 1090-2716 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method. In particular, we consider the framework of multi-level Monte Carlo for parametric expectations introduced in [24] and propose modifications of the MLMC estimator, error estimation procedure, and adaptive MLMC parameter selection to ensure the estimation of the CVaR and sensitivities for a given design with a prescribed accuracy. We then propose combining the MLMC framework with an alternating inexact minimisation-gradient descent algorithm, for which we prove Q-linear convergence in the optimisation iterations under the assumptions of strong convexity and Lipschitz continuity of the gradient of the objective function. We demonstrate the performance of our approach on two numerical examples of practical relevance, which evidence the same optimal asymptotic cost-tolerance behaviour as standard MLMC methods for fixed design computations of output expectations.
•Conditional-Value-at-Risk (CvaR) sensitivities using Parametric Expectations (PE).•Estimating sensitivities using Multi-Level Monte Carlo (MLMC) for PE.•Alternating minimization gradient-descent algorithm using MLMC sensitivities.•Exponential convergence predicted and obtained in the optimization iterations. |
|---|---|
| AbstractList | In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input data, using gradient-based approaches in combination with the Multi-Level Monte Carlo (MLMC) method. In particular, we consider the framework of multi-level Monte Carlo for parametric expectations introduced in [24] and propose modifications of the MLMC estimator, error estimation procedure, and adaptive MLMC parameter selection to ensure the estimation of the CVaR and sensitivities for a given design with a prescribed accuracy. We then propose combining the MLMC framework with an alternating inexact minimisation-gradient descent algorithm, for which we prove Q-linear convergence in the optimisation iterations under the assumptions of strong convexity and Lipschitz continuity of the gradient of the objective function. We demonstrate the performance of our approach on two numerical examples of practical relevance, which evidence the same optimal asymptotic cost-tolerance behaviour as standard MLMC methods for fixed design computations of output expectations.
•Conditional-Value-at-Risk (CvaR) sensitivities using Parametric Expectations (PE).•Estimating sensitivities using Multi-Level Monte Carlo (MLMC) for PE.•Alternating minimization gradient-descent algorithm using MLMC sensitivities.•Exponential convergence predicted and obtained in the optimization iterations. |
| ArticleNumber | 112523 |
| Author | Nobile, Fabio Ganesh, Sundar |
| Author_xml | – sequence: 1 givenname: Sundar orcidid: 0000-0001-6477-3924 surname: Ganesh fullname: Ganesh, Sundar email: sundar.ganesh@epfl.ch – sequence: 2 givenname: Fabio orcidid: 0000-0002-8130-0114 surname: Nobile fullname: Nobile, Fabio email: fabio.nobile@epfl.ch |
| BookMark | eNp9kM1KAzEUhYNUsK0-gLt5gYz5mV9cSdEqVNx0HzLJjc2YmZQkLfj2TltXLlwduJzvwvkWaDb6ERC6pySnhFYPfd6rfc4I4zmlrGT8Cs0paQlmNa1maE4Io7htW3qDFjH2hJCmLJo5gnWQ2sKYcCcj6Mzvkx1slMn6MfMmSzvIlB-1PR2kw0fpDoBlwsHGr-wQ7fh57gwHlyx2cASXvfsxQbaSwflsgLTz-hZdG-ki3P3mEm1fnrerV7z5WL-tnjZY8YIkbFRBDTSs6yjvNIDuSs24YpWBDpqO6qqqdVWaxtSyNY2SitecEFM0ujW65ktUX96q4GMMYISy6TwlBWmdoEScZIleTLLESZa4yJpI-ofcBzvI8P0v83hhYFp0tBBEVJNJBdoGUElob_-hfwBDQYcn |
| CitedBy_id | crossref_primary_10_1137_23M157956X |
| Cites_doi | 10.1159/000089933 10.1113/jphysiol.1952.sp004764 10.1287/opre.1070.0496 10.1016/j.cma.2022.115371 10.1159/000089932 10.1093/biomet/66.3.605 10.1287/mnsc.1080.0901 10.1287/moor.1050.0186 10.1016/S0006-3495(61)86902-6 10.1615/Int.J.UncertaintyQuantification.2023045259 10.1137/140964552 10.1016/j.jcp.2020.109466 10.1137/17M1122992 10.1145/3242094 10.1016/j.camwa.2017.02.028 10.1137/17M1135566 10.1137/S0895479899358194 10.1093/imanum/drac083 10.1111/1467-9965.00068 10.1109/JRPROC.1962.288235 10.1137/17M1155892 10.1007/s10107-012-0572-5 10.1137/140954556 10.2514/1.C035054 10.1016/S0378-4266(02)00271-6 10.1007/s10589-008-9196-3 10.1137/17M1154679 10.1017/S096249291500001X |
| ContentType | Journal Article |
| Copyright | 2023 The Authors |
| Copyright_xml | – notice: 2023 The Authors |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.jcp.2023.112523 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EISSN | 1090-2716 |
| ExternalDocumentID | 10_1016_j_jcp_2023_112523 S0021999123006186 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 6I. 6OB 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAXUO AAYFN ABBOA ABFRF ABJNI ABMAC ABNEU ABYKQ ACBEA ACDAQ ACFVG ACGFO ACGFS ACNCT ACRLP ACZNC ADBBV ADEZE AEBSH AEFWE AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHZHX AIALX AIEXJ AIKHN AITUG AIVDX AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD AXJTR BKOJK BLXMC CS3 DM4 DU5 EBS EFBJH EFLBG EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HLZ HVGLF IHE J1W K-O KOM LG5 LX9 LZ4 M37 M41 MO0 N9A O-L O9- OAUVE OGIMB OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SPD SSQ SSV SSZ T5K TN5 UPT YQT ZMT ZU3 ~02 ~G- 29K 6TJ 8WZ 9DU A6W AAQXK AATTM AAXKI AAYWO AAYXX ABFNM ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADFGL ADIYS ADJOM ADMUD ADNMO AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN BBWZM CAG CITATION COF D-I EFKBS EJD FGOYB G-2 HME HMV HZ~ NDZJH R2- SBC SHN SPG T9H UQL WUQ ZY4 ~HD |
| ID | FETCH-LOGICAL-c340t-fc41fe82bb13bdeedb5d23c26febe8b1d667d65f8f7a9f8cac37300f48d9fd73 |
| ISICitedReferencesCount | 3 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001137363700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0021-9991 |
| IngestDate | Sat Nov 29 03:10:41 EST 2025 Tue Nov 18 22:30:31 EST 2025 Fri Feb 23 02:33:54 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Uncertainty quantification Gradient descent CVaR Multilevel Monte Carlo methods VaR Optimisation under uncertainty |
| Language | English |
| License | This is an open access article under the CC BY license. |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c340t-fc41fe82bb13bdeedb5d23c26febe8b1d667d65f8f7a9f8cac37300f48d9fd73 |
| ORCID | 0000-0001-6477-3924 0000-0002-8130-0114 |
| OpenAccessLink | https://dx.doi.org/10.1016/j.jcp.2023.112523 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_jcp_2023_112523 crossref_primary_10_1016_j_jcp_2023_112523 elsevier_sciencedirect_doi_10_1016_j_jcp_2023_112523 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-12-15 |
| PublicationDateYYYYMMDD | 2023-12-15 |
| PublicationDate_xml | – month: 12 year: 2023 text: 2023-12-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of computational physics |
| PublicationYear | 2023 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Amestoy, Duff, Koster, L'Excellent (br0030) 2001; 23 Giles (br0160) 2008; 56 Quagliarella (br0330) 2019 Hong, Liu (br0200) 2011 Guth, Kaarnioja, Kuo, Schillings, Sloan (br0170) 2022 Giles (br0150) 2015; 24 Hodgkin, Huxley (br0180) 1952; 117 Krumscheid, Nobile, Pisaroni (br0250) 2020; 414 Ayoul-Guilmard, Ganesh, Nobile (br0060) July 27, 2020 Chaudhuri, Peherstorfer, Willcox (br0110) 2020 Kouri, Surowiec (br0230) 2016; 26 Quagliarella, Tirado, Bornaccioni (br0340) 2020 Lim, Sherali, Uryasev (br0260) 2010; 46 Krumscheid, Nobile (br0240) 2018; 6 Beiser, Keith, Urbainczyk, Wohlmuth (br0070) 2023 Uzunca, Küçükseyhan, Yücel, Karasözen (br0390) 2017; 73 Van Barel, Vandewalle (br0400) 2019; 7 Pisaroni, Nobile, Leyland (br0320) 2019; 56 Ayoul-Guilmard, Ganesh, Krumscheid, Nobile (br0050) 2023; 13 Hoel, von Schwerin, Szepessy, Tempone (br0190) 2012 Peherstorfer, Kramer, Willcox (br0310) 2018; 6 Ermakova, Panteleev, Shnol (br0130) 2005; 34 Ruszczyński, Shapiro (br0360) 2006; 31 Kodakkal, Keith, Khristenko, Apostolatos, Bletzinger, Wohlmuth, Wüchner (br0220) 2022; 402 Scott (br0370) 1979; 66 FitzHugh (br0140) 1961; 1 Collier, Haji-Ali, Nobile, von Schwerin, Tempone (br0120) 2014 Breiten, Kunisch (br0090) 2014; 52 Martin, Nobile, Tsilifis (br0290) 2019 Hong, Liu (br0210) 2009; 55 Shapiro, Dentcheva, Ruszczyński (br0380) 2009 Nagumo, Arimoto, Yoshizawa (br0300) 1962; 50 Amela, Ayoul-Guilmard, Badia, Ganesh, Nobile, Rossi, Tosi (br0010) Oct. 2020 Artzner, Delbaen, Eber, Heath (br0040) 1999; 9 Amestoy, Buttari, L'Excellent, Mary (br0020) 1 2019; 45 Bollapragada, Byrd, Nocedal (br0080) 2018; 28 Tyrrell Rockafellar, Uryasev (br0350) 2002; 26 Byrd, Chin, Nocedal, Wu (br0100) 2012; 134 Lobanov, Starozhilova (br0270) 2005; 34 Logg, Mardal, Wells (br0280) 2012 Ermakova (10.1016/j.jcp.2023.112523_br0130) 2005; 34 Quagliarella (10.1016/j.jcp.2023.112523_br0340) 2020 Giles (10.1016/j.jcp.2023.112523_br0160) 2008; 56 Amestoy (10.1016/j.jcp.2023.112523_br0020) 2019; 45 Kodakkal (10.1016/j.jcp.2023.112523_br0220) 2022; 402 Lim (10.1016/j.jcp.2023.112523_br0260) 2010; 46 Nagumo (10.1016/j.jcp.2023.112523_br0300) 1962; 50 Collier (10.1016/j.jcp.2023.112523_br0120) 2014 Ayoul-Guilmard (10.1016/j.jcp.2023.112523_br0060) 2020 Logg (10.1016/j.jcp.2023.112523_br0280) 2012 Beiser (10.1016/j.jcp.2023.112523_br0070) 2023 FitzHugh (10.1016/j.jcp.2023.112523_br0140) 1961; 1 Hong (10.1016/j.jcp.2023.112523_br0200) 2011 Hodgkin (10.1016/j.jcp.2023.112523_br0180) 1952; 117 Giles (10.1016/j.jcp.2023.112523_br0150) 2015; 24 Kouri (10.1016/j.jcp.2023.112523_br0230) 2016; 26 Tyrrell Rockafellar (10.1016/j.jcp.2023.112523_br0350) 2002; 26 Uzunca (10.1016/j.jcp.2023.112523_br0390) 2017; 73 Van Barel (10.1016/j.jcp.2023.112523_br0400) 2019; 7 Lobanov (10.1016/j.jcp.2023.112523_br0270) 2005; 34 Artzner (10.1016/j.jcp.2023.112523_br0040) 1999; 9 Chaudhuri (10.1016/j.jcp.2023.112523_br0110) 2020 Martin (10.1016/j.jcp.2023.112523_br0290) Bollapragada (10.1016/j.jcp.2023.112523_br0080) 2018; 28 Breiten (10.1016/j.jcp.2023.112523_br0090) 2014; 52 Guth (10.1016/j.jcp.2023.112523_br0170) Hoel (10.1016/j.jcp.2023.112523_br0190) 2012 Krumscheid (10.1016/j.jcp.2023.112523_br0240) 2018; 6 Ayoul-Guilmard (10.1016/j.jcp.2023.112523_br0050) 2023; 13 Amestoy (10.1016/j.jcp.2023.112523_br0030) 2001; 23 Krumscheid (10.1016/j.jcp.2023.112523_br0250) 2020; 414 Quagliarella (10.1016/j.jcp.2023.112523_br0330) 2019 Byrd (10.1016/j.jcp.2023.112523_br0100) 2012; 134 Peherstorfer (10.1016/j.jcp.2023.112523_br0310) 2018; 6 Shapiro (10.1016/j.jcp.2023.112523_br0380) 2009 Scott (10.1016/j.jcp.2023.112523_br0370) 1979; 66 Amela (10.1016/j.jcp.2023.112523_br0010) 2020 Pisaroni (10.1016/j.jcp.2023.112523_br0320) 2019; 56 Ruszczyński (10.1016/j.jcp.2023.112523_br0360) 2006; 31 Hong (10.1016/j.jcp.2023.112523_br0210) 2009; 55 |
| References_xml | – volume: 28 start-page: 3312 year: 2018 end-page: 3343 ident: br0080 article-title: Adaptive sampling strategies for stochastic optimization publication-title: SIAM J. Optim. – volume: 6 start-page: 1256 year: 2018 end-page: 1293 ident: br0240 article-title: Multilevel Monte Carlo approximation of functions publication-title: SIAM/ASA J. Uncertain. Quantificat. – start-page: 541 year: 2019 end-page: 565 ident: br0330 article-title: Value-at-risk and conditional value-at-risk in optimization under uncertainty publication-title: Uncertainty Management for Robust Industrial Design in Aeronautics – year: 2019 ident: br0290 article-title: A multilevel stochastic gradient method for PDE-constrained optimal control problems with uncertain parameters – volume: 73 start-page: 2151 year: 2017 end-page: 2169 ident: br0390 article-title: Optimal control of convective FitzHugh–Nagumo equation publication-title: Comput. Math. Appl. – volume: 52 start-page: 4057 year: 2014 end-page: 4081 ident: br0090 article-title: Riccati-based feedback control of the monodomain equations with the Fitzhugh–Nagumo model publication-title: SIAM J. Control Optim. – year: 2012 ident: br0280 article-title: Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, vol. 84 – volume: 56 start-page: 607 year: 2008 end-page: 617 ident: br0160 article-title: Multilevel Monte Carlo path simulation publication-title: Oper. Res. – volume: 117 start-page: 500 year: 1952 end-page: 544 ident: br0180 article-title: A quantitative description of membrane current and its application to conduction and excitation in nerve publication-title: J. Physiol. – start-page: 217 year: 2012 end-page: 234 ident: br0190 article-title: Adaptive multilevel Monte Carlo simulation publication-title: Numerical Analysis of Multiscale Computations – volume: 56 start-page: 771 year: 2019 end-page: 786 ident: br0320 article-title: Continuation multilevel Monte Carlo evolutionary algorithm for robust aerodynamic shape design publication-title: J. Aircr. – year: July 27, 2020 ident: br0060 article-title: Report on stochastic optimisation for simple problems – volume: 134 start-page: 127 year: 2012 end-page: 155 ident: br0100 article-title: Sample size selection in optimization methods for machine learning publication-title: Math. Program. – volume: 66 start-page: 605 year: 1979 end-page: 610 ident: br0370 article-title: On optimal and data-based histograms publication-title: Biometrika – volume: 1 start-page: 445 year: 1961 end-page: 466 ident: br0140 article-title: Impulses and physiological states in theoretical models of nerve membrane publication-title: Biophys. J. – volume: 13 start-page: 61 year: 2023 end-page: 98 ident: br0050 article-title: Quantifying uncertain system outputs via the multilevel Monte Carlo method — distribution and robustness measures publication-title: Int. J. Uncertain. Quantificat. – year: 2009 ident: br0380 article-title: Lectures on Stochastic Programming: Modeling and Theory – start-page: 1 year: 2014 end-page: 34 ident: br0120 article-title: A continuation multilevel Monte Carlo algorithm publication-title: BIT Numer. Math. – volume: 9 start-page: 203 year: 1999 end-page: 228 ident: br0040 article-title: Coherent measures of risk publication-title: Math. Finance – year: 2023 ident: br0070 article-title: Adaptive sampling strategies for risk-averse stochastic optimization with constraints publication-title: IMA J. Numer. Anal. – volume: 24 start-page: 259 year: 2015 end-page: 328 ident: br0150 article-title: Multilevel Monte Carlo methods publication-title: Acta Numer. – volume: 7 start-page: 174 year: 2019 end-page: 202 ident: br0400 article-title: Robust optimization of PDEs with random coefficients using a multilevel Monte Carlo method publication-title: SIAM/ASA J. Uncertain. Quantificat. – volume: 34 start-page: 135 year: 2005 end-page: 142 ident: br0130 article-title: Blood coagulation and propagation of autowaves in flow publication-title: Pathophysiol. Haemost. Thromb. – volume: 31 start-page: 433 year: 2006 end-page: 452 ident: br0360 article-title: Optimization of convex risk functions publication-title: Math. Oper. Res. – start-page: 153 year: 2020 end-page: 168 ident: br0340 article-title: Risk measures applied to robust aerodynamic shape design optimization publication-title: Flexible Engineering Toward Green Aircraft – volume: 50 start-page: 2061 year: 1962 end-page: 2070 ident: br0300 article-title: An active pulse transmission line simulating nerve axon publication-title: Proc. IRE – volume: 6 start-page: 737 year: 2018 end-page: 761 ident: br0310 article-title: Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation publication-title: SIAM/ASA J. Uncertain. Quantificat. – volume: 34 start-page: 121 year: 2005 end-page: 134 ident: br0270 article-title: The effect of convective flows on blood coagulation processes publication-title: Pathophysiol. Haemost. Thromb. – start-page: 2129 year: 2020 ident: br0110 article-title: Multifidelity cross-entropy estimation of conditional value-at-risk for risk-averse design optimization publication-title: AIAA Scitech 2020 Forum – volume: 402 year: 2022 ident: br0220 article-title: Risk-averse design of tall buildings for uncertain wind conditions publication-title: Comput. Methods Appl. Mech. Eng. – year: Oct. 2020 ident: br0010 article-title: ExaQUte XMC – volume: 26 start-page: 1443 year: 2002 end-page: 1471 ident: br0350 article-title: Conditional value-at-risk for general loss distributions publication-title: J. Bank. Finance – volume: 414 year: 2020 ident: br0250 article-title: Quantifying uncertain system outputs via the multilevel Monte Carlo method—Part I: central moment estimation publication-title: J. Comput. Phys. – start-page: 95 year: 2011 end-page: 107 ident: br0200 article-title: Monte Carlo estimation of value-at-risk, conditional value-at-risk and their sensitivities publication-title: Proceedings of the 2011 Winter Simulation Conference (WSC) – volume: 46 start-page: 391 year: 2010 end-page: 415 ident: br0260 article-title: Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization publication-title: Comput. Optim. Appl. – volume: 26 start-page: 365 year: 2016 end-page: 396 ident: br0230 article-title: Risk-averse PDE-constrained optimization using the conditional value-at-risk publication-title: SIAM J. Optim. – volume: 23 start-page: 15 year: 2001 end-page: 41 ident: br0030 article-title: A fully asynchronous multifrontal solver using distributed dynamic scheduling publication-title: SIAM J. Matrix Anal. Appl. – year: 2022 ident: br0170 article-title: Parabolic PDE-constrained optimal control under uncertainty with entropic risk measure using quasi-Monte Carlo integration – volume: 45 start-page: 2:1 year: 1 2019 end-page: 2:26 ident: br0020 article-title: Performance and scalability of the block low-rank multifrontal factorization on multicore architectures publication-title: ACM Trans. Math. Softw. – volume: 55 start-page: 281 year: 2009 end-page: 293 ident: br0210 article-title: Simulating sensitivities of conditional value at risk publication-title: Manag. Sci. – volume: 34 start-page: 135 issue: 2–3 year: 2005 ident: 10.1016/j.jcp.2023.112523_br0130 article-title: Blood coagulation and propagation of autowaves in flow publication-title: Pathophysiol. Haemost. Thromb. doi: 10.1159/000089933 – volume: 117 start-page: 500 issue: 4 year: 1952 ident: 10.1016/j.jcp.2023.112523_br0180 article-title: A quantitative description of membrane current and its application to conduction and excitation in nerve publication-title: J. Physiol. doi: 10.1113/jphysiol.1952.sp004764 – volume: 56 start-page: 607 issue: 3 year: 2008 ident: 10.1016/j.jcp.2023.112523_br0160 article-title: Multilevel Monte Carlo path simulation publication-title: Oper. Res. doi: 10.1287/opre.1070.0496 – ident: 10.1016/j.jcp.2023.112523_br0170 – year: 2012 ident: 10.1016/j.jcp.2023.112523_br0280 – volume: 402 year: 2022 ident: 10.1016/j.jcp.2023.112523_br0220 article-title: Risk-averse design of tall buildings for uncertain wind conditions publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2022.115371 – volume: 34 start-page: 121 issue: 2–3 year: 2005 ident: 10.1016/j.jcp.2023.112523_br0270 article-title: The effect of convective flows on blood coagulation processes publication-title: Pathophysiol. Haemost. Thromb. doi: 10.1159/000089932 – volume: 66 start-page: 605 issue: 3 year: 1979 ident: 10.1016/j.jcp.2023.112523_br0370 article-title: On optimal and data-based histograms publication-title: Biometrika doi: 10.1093/biomet/66.3.605 – volume: 55 start-page: 281 issue: 2 year: 2009 ident: 10.1016/j.jcp.2023.112523_br0210 article-title: Simulating sensitivities of conditional value at risk publication-title: Manag. Sci. doi: 10.1287/mnsc.1080.0901 – year: 2020 ident: 10.1016/j.jcp.2023.112523_br0060 – volume: 31 start-page: 433 issue: 3 year: 2006 ident: 10.1016/j.jcp.2023.112523_br0360 article-title: Optimization of convex risk functions publication-title: Math. Oper. Res. doi: 10.1287/moor.1050.0186 – volume: 1 start-page: 445 issue: 6 year: 1961 ident: 10.1016/j.jcp.2023.112523_br0140 article-title: Impulses and physiological states in theoretical models of nerve membrane publication-title: Biophys. J. doi: 10.1016/S0006-3495(61)86902-6 – volume: 13 start-page: 61 issue: 5 year: 2023 ident: 10.1016/j.jcp.2023.112523_br0050 article-title: Quantifying uncertain system outputs via the multilevel Monte Carlo method — distribution and robustness measures publication-title: Int. J. Uncertain. Quantificat. doi: 10.1615/Int.J.UncertaintyQuantification.2023045259 – start-page: 217 year: 2012 ident: 10.1016/j.jcp.2023.112523_br0190 article-title: Adaptive multilevel Monte Carlo simulation – year: 2009 ident: 10.1016/j.jcp.2023.112523_br0380 – volume: 52 start-page: 4057 issue: 6 year: 2014 ident: 10.1016/j.jcp.2023.112523_br0090 article-title: Riccati-based feedback control of the monodomain equations with the Fitzhugh–Nagumo model publication-title: SIAM J. Control Optim. doi: 10.1137/140964552 – volume: 414 year: 2020 ident: 10.1016/j.jcp.2023.112523_br0250 article-title: Quantifying uncertain system outputs via the multilevel Monte Carlo method—Part I: central moment estimation publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2020.109466 – volume: 6 start-page: 737 issue: 2 year: 2018 ident: 10.1016/j.jcp.2023.112523_br0310 article-title: Multifidelity preconditioning of the cross-entropy method for rare event simulation and failure probability estimation publication-title: SIAM/ASA J. Uncertain. Quantificat. doi: 10.1137/17M1122992 – start-page: 153 year: 2020 ident: 10.1016/j.jcp.2023.112523_br0340 article-title: Risk measures applied to robust aerodynamic shape design optimization – volume: 45 start-page: 2:1 year: 2019 ident: 10.1016/j.jcp.2023.112523_br0020 article-title: Performance and scalability of the block low-rank multifrontal factorization on multicore architectures publication-title: ACM Trans. Math. Softw. doi: 10.1145/3242094 – volume: 73 start-page: 2151 issue: 9 year: 2017 ident: 10.1016/j.jcp.2023.112523_br0390 article-title: Optimal control of convective FitzHugh–Nagumo equation publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2017.02.028 – volume: 6 start-page: 1256 issue: 3 year: 2018 ident: 10.1016/j.jcp.2023.112523_br0240 article-title: Multilevel Monte Carlo approximation of functions publication-title: SIAM/ASA J. Uncertain. Quantificat. doi: 10.1137/17M1135566 – volume: 23 start-page: 15 issue: 1 year: 2001 ident: 10.1016/j.jcp.2023.112523_br0030 article-title: A fully asynchronous multifrontal solver using distributed dynamic scheduling publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479899358194 – year: 2023 ident: 10.1016/j.jcp.2023.112523_br0070 article-title: Adaptive sampling strategies for risk-averse stochastic optimization with constraints publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drac083 – volume: 9 start-page: 203 issue: 3 year: 1999 ident: 10.1016/j.jcp.2023.112523_br0040 article-title: Coherent measures of risk publication-title: Math. Finance doi: 10.1111/1467-9965.00068 – volume: 50 start-page: 2061 issue: 10 year: 1962 ident: 10.1016/j.jcp.2023.112523_br0300 article-title: An active pulse transmission line simulating nerve axon publication-title: Proc. IRE doi: 10.1109/JRPROC.1962.288235 – start-page: 541 year: 2019 ident: 10.1016/j.jcp.2023.112523_br0330 article-title: Value-at-risk and conditional value-at-risk in optimization under uncertainty – start-page: 95 year: 2011 ident: 10.1016/j.jcp.2023.112523_br0200 article-title: Monte Carlo estimation of value-at-risk, conditional value-at-risk and their sensitivities – volume: 7 start-page: 174 issue: 1 year: 2019 ident: 10.1016/j.jcp.2023.112523_br0400 article-title: Robust optimization of PDEs with random coefficients using a multilevel Monte Carlo method publication-title: SIAM/ASA J. Uncertain. Quantificat. doi: 10.1137/17M1155892 – volume: 134 start-page: 127 issue: 1 year: 2012 ident: 10.1016/j.jcp.2023.112523_br0100 article-title: Sample size selection in optimization methods for machine learning publication-title: Math. Program. doi: 10.1007/s10107-012-0572-5 – volume: 26 start-page: 365 issue: 1 year: 2016 ident: 10.1016/j.jcp.2023.112523_br0230 article-title: Risk-averse PDE-constrained optimization using the conditional value-at-risk publication-title: SIAM J. Optim. doi: 10.1137/140954556 – volume: 56 start-page: 771 issue: 2 year: 2019 ident: 10.1016/j.jcp.2023.112523_br0320 article-title: Continuation multilevel Monte Carlo evolutionary algorithm for robust aerodynamic shape design publication-title: J. Aircr. doi: 10.2514/1.C035054 – start-page: 2129 year: 2020 ident: 10.1016/j.jcp.2023.112523_br0110 article-title: Multifidelity cross-entropy estimation of conditional value-at-risk for risk-averse design optimization – ident: 10.1016/j.jcp.2023.112523_br0290 – year: 2020 ident: 10.1016/j.jcp.2023.112523_br0010 – volume: 26 start-page: 1443 issue: 7 year: 2002 ident: 10.1016/j.jcp.2023.112523_br0350 article-title: Conditional value-at-risk for general loss distributions publication-title: J. Bank. Finance doi: 10.1016/S0378-4266(02)00271-6 – volume: 46 start-page: 391 issue: 3 year: 2010 ident: 10.1016/j.jcp.2023.112523_br0260 article-title: Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-008-9196-3 – volume: 28 start-page: 3312 issue: 4 year: 2018 ident: 10.1016/j.jcp.2023.112523_br0080 article-title: Adaptive sampling strategies for stochastic optimization publication-title: SIAM J. Optim. doi: 10.1137/17M1154679 – start-page: 1 year: 2014 ident: 10.1016/j.jcp.2023.112523_br0120 article-title: A continuation multilevel Monte Carlo algorithm publication-title: BIT Numer. Math. – volume: 24 start-page: 259 year: 2015 ident: 10.1016/j.jcp.2023.112523_br0150 article-title: Multilevel Monte Carlo methods publication-title: Acta Numer. doi: 10.1017/S096249291500001X |
| SSID | ssj0008548 |
| Score | 2.4530272 |
| Snippet | In this work, we tackle the problem of minimising the Conditional-Value-at-Risk (CVaR) of output quantities of complex differential models with random input... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 112523 |
| SubjectTerms | CVaR Gradient descent Multilevel Monte Carlo methods Optimisation under uncertainty Uncertainty quantification VaR |
| Title | Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method |
| URI | https://dx.doi.org/10.1016/j.jcp.2023.112523 |
| Volume | 495 |
| WOSCitedRecordID | wos001137363700001&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: 1090-2716 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008548 issn: 0021-9991 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELaWlgMXKC_1AcgHTiBXSZzE9rFCfcChQmIPe4viR8SulqTaTav-fMYZO2wLiwCJS7SK4mQ182VmPPlmhpC3qdPCB8JMy5yznGsOdtBK5lxuISAHh6hw2IS4vJSzmfo8mXyJtTA3S9G28vZWXf1XVcM5ULYvnf0LdY83hRPwG5QOR1A7HP9I8eergcXVM--g7PsObMK3wNmJhADYA9s5JgGZ7_btWN2zgWR-vY7lUwPTkC09p8i_-L3z3JBlF0ZOb4lpzTAjIuYXMWsyBu3nNZjVr0gF8umLMQ_d6TmSms9qjbSwmIfIuOd0YCUmJsdigcwd_iYyQBQO5Dp2aGMTlbBMYIllNMI5jtr8yaBjbmFxvDC-uWjGfclTgRXK9_pk-8_OvqcCuGIfl8nyAdnNRKHAWu-efDydfRodtCxydNDhv8WP3QPt796Dfh2ubIQg0z3yOMiZnqDOn5KJa5-RJ2EfQYOVXj8n7i4E6CYEaNdQUC_dCgE6QGC4ZgMCdIAAHSBAEQIvyPTsdPrhgoVxGszwPOlZY_K0cTLTOuXaQmykC5txk5UNvMhSp7YshS2LRjaiVo00teF-mEGTS6saK_hLstN2rdsnNDXC6rp0xsHuPa1rmXCrLGz0UwOrtTggSRRaZUKreT_xZFlFTuGiAjlXXs4VyvmAvBuXXGGfld9dnEdNVCFQxACwAthsX3b4b8uOyKMfeH9FdvrVtXtNHpqbfr5evQng-g4gL4_K |
| 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=Gradient-based+optimisation+of+the+conditional-value-at-risk+using+the+multi-level+Monte+Carlo+method&rft.jtitle=Journal+of+computational+physics&rft.au=Ganesh%2C+Sundar&rft.au=Nobile%2C+Fabio&rft.date=2023-12-15&rft.pub=Elsevier+Inc&rft.issn=0021-9991&rft.eissn=1090-2716&rft.volume=495&rft_id=info:doi/10.1016%2Fj.jcp.2023.112523&rft.externalDocID=S0021999123006186 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0021-9991&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0021-9991&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0021-9991&client=summon |