Barrier methods based on Jordan–Hilbert algebras for stochastic optimization in spin factors
Infinite-dimensional stochastic second-order cone programming involves minimizing linear functions over intersections of affine linear manifolds with infinite-dimensional second-order cones. However, even though there is a legitimate necessity to explore these methods in general spaces, there is an...
Gespeichert in:
| Veröffentlicht in: | R.A.I.R.O. Recherche opérationnelle Jg. 58; H. 1; S. 1011 - 1044 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
01.01.2024
|
| ISSN: | 0399-0559, 2804-7303 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Infinite-dimensional stochastic second-order cone programming involves minimizing linear functions over intersections of affine linear manifolds with infinite-dimensional second-order cones. However, even though there is a legitimate necessity to explore these methods in general spaces, there is an absence of infinite-dimensional counterparts for these methods. In this paper, we present decomposition logarithmic-barrier interior-point methods based on unital Jordan–Hilbert algebras for this class of optimization problems in the infinite-dimensional setting. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best-known complexity obtained by such methods for the finite-dimensional setting. We apply our results to an important problem in stochastic control, namely the two-stage stochastic multi-criteria design problem. We show that the corresponding infinite-dimensional system in this case is a matrix differential Ricatti equation plus a finite-dimensional system, and hence, it can be solved efficiently to find the search direction. |
|---|---|
| AbstractList | Infinite-dimensional stochastic second-order cone programming involves minimizing linear functions over intersections of affine linear manifolds with infinite-dimensional second-order cones. However, even though there is a legitimate necessity to explore these methods in general spaces, there is an absence of infinite-dimensional counterparts for these methods. In this paper, we present decomposition logarithmic-barrier interior-point methods based on unital Jordan–Hilbert algebras for this class of optimization problems in the infinite-dimensional setting. The results show that the iteration complexity of the proposed algorithms is independent on the choice of Hilbert spaces from which the underlying spin factors are formed, and so it coincides with the best-known complexity obtained by such methods for the finite-dimensional setting. We apply our results to an important problem in stochastic control, namely the two-stage stochastic multi-criteria design problem. We show that the corresponding infinite-dimensional system in this case is a matrix differential Ricatti equation plus a finite-dimensional system, and hence, it can be solved efficiently to find the search direction. |
| Author | Alzalg, Baha |
| Author_xml | – sequence: 1 givenname: Baha orcidid: 0000-0002-1839-8083 surname: Alzalg fullname: Alzalg, Baha |
| BookMark | eNotkDFOAzEURC0UJEJIwwlcIy35tte73hIiIKBINNCy-rb_EkvJOrLdQMUduCEnIYg0M828Kd45m4xxJMYuBVwL0GKR4kKCVKIzJ2wqDdRVq0BN2BRU11WgdXfG5jkHexibpulAT9nbLaYUKPEdlU30mVvM5Hkc-VNMHsefr-9V2FpKheP2nWzCzIeYeC7RbTCX4Hjcl7ALn1jCgQojz_tDDOhKTPmCnQ64zTQ_9oy93t-9LFfV-vnhcXmzrpyUTancIIwD1MoK15D3WlHryTvhpbOts42vJZqWtIcWZQPUCks4DNYarA2AmrGr_1-XYs6Jhn6fwg7TRy-g_5PTp9gf5ahf7x5c_w |
| Cites_doi | 10.1007/s10957-022-02128-6 10.1137/0806020 10.1007/s10107-003-0380-z 10.1287/opre.1080.0659 10.1109/ACCESS.2019.2962840 10.1016/j.jmaa.2013.07.075 10.3934/dcds.1998.4.653 10.1007/s11356-022-20713-0 10.1007/s10479-022-05119-y 10.1016/j.jalgebra.2017.08.017 10.1016/j.amc.2004.04.095 10.1137/080742026 10.1007/s10107-002-0339-5 10.1007/s002459900054 10.1007/s40815-021-01209-4 10.1016/j.amc.2015.05.014 10.1137/050622067 10.1007/PL00011433 10.1007/s10107-003-0471-x 10.1007/s10479-022-04829-7 10.1007/s00500-019-04010-6 10.1007/BFb0089281 10.1007/s10107-003-0424-4 10.1007/s10957-013-0428-z 10.1080/02331934.2018.1533553 10.1016/j.amc.2014.10.015 10.1080/01630563.2019.1709499 10.1137/1.9781611970791 10.1137/S1052623495293056 10.1090/S0025-5718-2010-02449-4 10.1016/j.amc.2006.08.171 10.1137/S1052623494269035 10.1007/BF02108300 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION |
| DOI | 10.1051/ro/2023198 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 2804-7303 |
| EndPage | 1044 |
| ExternalDocumentID | 10_1051_ro_2023198 |
| GroupedDBID | --K -E. .FH 0E1 123 1B1 4.4 5VS 74X 74Y 7~V 8FE 8FG AADXX AAFWJ AAOGA AAOTM AAYXX ABGDZ ABKKG ABNSH ABUBZ ABZDU ACACO ACGFS ACIMK ACIWK ACQPF ACRPL ACZPN ADNMO AEMTW AFAYI AFHSK AFUTZ AGQPQ AJPFC ALMA_UNASSIGNED_HOLDINGS AMVHM ARABE ASPBG AVWKF AZPVJ BPHCQ C0O CITATION CS3 DC4 EBS EJD FAM HG- HST HZ~ I-F I.6 IHE IL9 I~P J36 J38 J3A K60 K6V K6~ L6V L98 LO0 M-V M41 NIF O9- OAV P62 PQQKQ PROAC RCA ROL RPZ RR0 S6- WQ3 WXU |
| ID | FETCH-LOGICAL-c226t-cf18c0a53b1c6edd53e7dedc1d2cb7cb6d42a87e5d07a260e71beaffbb8a48003 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001177701100004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0399-0559 |
| IngestDate | Sat Nov 29 04:47:32 EST 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c226t-cf18c0a53b1c6edd53e7dedc1d2cb7cb6d42a87e5d07a260e71beaffbb8a48003 |
| ORCID | 0000-0002-1839-8083 |
| OpenAccessLink | https://doi.org/10.1051/ro/2023198 |
| PageCount | 34 |
| ParticipantIDs | crossref_primary_10_1051_ro_2023198 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-01-01 |
| PublicationDateYYYYMMDD | 2024-01-01 |
| PublicationDate_xml | – month: 01 year: 2024 text: 2024-01-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | R.A.I.R.O. Recherche opérationnelle |
| PublicationYear | 2024 |
| References | Schmieta (R30) 2003; 96 Zhao (R17) 2001; 90 Faybusovich (R2) 2003; 97 Goli (R5) 2023; 328 Alzalg (R14) 2014; 409 Chen (R27) 2011; 21 Lotfi (R10) 2022; 24 Alzalg (R25) 2022; 196 Alzalg (R8) 2014; 163 Chu (R13) 2017; 491 Alzalg (R16) 2018; 163 Ariyawansa (R24) 2011; 80 Lotfi (R11) 2022; 29 Kojima (R33) 1997; 7 R29 Zhao (R26) 2005; 102 Sangaiah (R6) 2020; 24 Renegar (R3) 1995; 70 Alzalg (R22) 2018; 67 Mehrotra (R23) 2007; 18 Helmberg (R31) 1996; 6 Lim (R1) 1998; 4 Alzalg (R28) 2020; 41 Alzalg (R7) 2014; 249 Alizadeh (R39) 2003; 95 Lotfi (R9) 2021; 1 R12 Alzalg (R21) 2020; 80 R34 R36 R35 Faybusovich (R4) 1997; 36 R37 Cho (R18) 2005; 164 Alzalg (R15) 2015; 256 Nomura (R38) 1994; 12 Mehrotra (R19) 2009; 57 Monteiro (R32) 1997; 7 Ariyawansa (R20) 2007; 186 |
| References_xml | – volume: 70 start-page: 279 year: 1995 ident: R3 publication-title: Math. Program – volume: 196 start-page: 490 year: 2022 ident: R25 publication-title: J. Optim. Theory App doi: 10.1007/s10957-022-02128-6 – volume: 1 start-page: 1367 year: 2021 ident: R9 publication-title: Int. J. Logist. Res. Appl – volume: 6 start-page: 342 year: 1996 ident: R31 publication-title: SIAM J. Optim doi: 10.1137/0806020 – volume: 96 start-page: 409 year: 2003 ident: R30 publication-title: Math. Program. Ser. A doi: 10.1007/s10107-003-0380-z – volume: 57 start-page: 964 year: 2009 ident: R19 publication-title: Oper. Res doi: 10.1287/opre.1080.0659 – volume: 80 start-page: 4995 year: 2020 ident: R21 publication-title: IEEE Access doi: 10.1109/ACCESS.2019.2962840 – volume: 409 start-page: 973 year: 2014 ident: R14 publication-title: J. Math. Anal. App doi: 10.1016/j.jmaa.2013.07.075 – volume: 4 start-page: 653 year: 1998 ident: R1 publication-title: Discrete Cont. Dyn. Syst doi: 10.3934/dcds.1998.4.653 – volume: 29 start-page: 70285 year: 2022 ident: R11 publication-title: Environ. Sci. Pollut. Res doi: 10.1007/s11356-022-20713-0 – ident: R12 doi: 10.1007/s10479-022-05119-y – volume: 491 start-page: 357 year: 2017 ident: R13 publication-title: J. Algebra doi: 10.1016/j.jalgebra.2017.08.017 – volume: 164 start-page: 45 year: 2005 ident: R18 publication-title: Appl. Math. Comput doi: 10.1016/j.amc.2004.04.095 – volume: 21 start-page: 1667 year: 2011 ident: R27 publication-title: SIAM J. Optim doi: 10.1137/080742026 – volume: 95 start-page: 3 year: 2003 ident: R39 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-002-0339-5 – volume: 36 start-page: 43 year: 1997 ident: R4 publication-title: Appl. Math. Optim doi: 10.1007/s002459900054 – volume: 24 start-page: 1216 year: 2022 ident: R10 publication-title: Int. J. Fuzzy Syst doi: 10.1007/s40815-021-01209-4 – volume: 256 start-page: 494 year: 2015 ident: R15 publication-title: Appl. Math. Comput doi: 10.1016/j.amc.2015.05.014 – volume: 18 start-page: 206 year: 2007 ident: R23 publication-title: SIAM J. Optim doi: 10.1137/050622067 – volume: 90 start-page: 507 year: 2001 ident: R17 publication-title: Math. Program. Ser. A doi: 10.1007/PL00011433 – volume: 102 start-page: 1 year: 2005 ident: R26 publication-title: Math. Program doi: 10.1007/s10107-003-0471-x – ident: R35 – volume: 328 start-page: 493 year: 2023 ident: R5 publication-title: Ann. Oper. Res doi: 10.1007/s10479-022-04829-7 – volume: 24 start-page: 7885 year: 2020 ident: R6 publication-title: Soft. Comput doi: 10.1007/s00500-019-04010-6 – ident: R37 doi: 10.1007/BFb0089281 – volume: 97 start-page: 471 year: 2003 ident: R2 publication-title: Math. Program. Ser. B doi: 10.1007/s10107-003-0424-4 – volume: 163 start-page: 148 year: 2018 ident: R16 publication-title: J. Optim. Theory Appl doi: 10.1007/s10957-013-0428-z – volume: 67 start-page: 2291 year: 2018 ident: R22 publication-title: Optimization doi: 10.1080/02331934.2018.1533553 – volume: 163 start-page: 148 year: 2014 ident: R8 publication-title: J. Optim. Theory Appl doi: 10.1007/s10957-013-0428-z – volume: 249 start-page: 1 year: 2014 ident: R7 publication-title: Appl. Math. Comput doi: 10.1016/j.amc.2014.10.015 – ident: R29 – volume: 41 start-page: 901 year: 2020 ident: R28 publication-title: Numer. Funct. Anal. Optim doi: 10.1080/01630563.2019.1709499 – ident: R34 doi: 10.1137/1.9781611970791 – volume: 7 start-page: 663 year: 1997 ident: R32 publication-title: SIAM J. Optim doi: 10.1137/S1052623495293056 – volume: 80 start-page: 1639 year: 2011 ident: R24 publication-title: Math. Comput doi: 10.1090/S0025-5718-2010-02449-4 – volume: 186 start-page: 1683 year: 2007 ident: R20 publication-title: Appl. Math. Comput doi: 10.1016/j.amc.2006.08.171 – volume: 7 start-page: 86 year: 1997 ident: R33 publication-title: SIAM J. Optim doi: 10.1137/S1052623494269035 – ident: R36 – volume: 12 start-page: 237 year: 1994 ident: R38 publication-title: Ann. Global Anal. Geom doi: 10.1007/BF02108300 |
| SSID | ssib051866905 ssib051327486 ssj0003353 ssib050921426 |
| Score | 2.2918193 |
| Snippet | Infinite-dimensional stochastic second-order cone programming involves minimizing linear functions over intersections of affine linear manifolds with... |
| SourceID | crossref |
| SourceType | Index Database |
| StartPage | 1011 |
| Title | Barrier methods based on Jordan–Hilbert algebras for stochastic optimization in spin factors |
| Volume | 58 |
| WOSCitedRecordID | wos001177701100004&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: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2804-7303 dateEnd: 99991231 omitProxy: false ssIdentifier: ssib051866905 issn: 0399-0559 databaseCode: M~E dateStart: 20010101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELagcIAD4inesgS3VdI4jmPnWFCrgqCgqqCeWPmVdiVwVtkFVT1U_Af-Ib-EcezsGsqhHDhstGttEsnzafzNjP0NQs8ppbUVRmbakiarrC4yCbQ0A_JhZOn1i4azVR_f8L09cXjYvI8J_cXQToA7J05Omvl_NTWMgbH90dl_MPfqoTAA38HocAWzw_VChn8h-6ELXegNvZj4dcr4msBriDOlG3c30N2Zl7fyGd8jXzwedBkmQAX1sfTazZMOnMmXeErTZ0UW85kb2_OklHY_38pf5fv5u9xzUIAAfODmUIEP-PJbadbQ-nwKrwy1jmOZZh3KKsk6xNNWXr2ARTVvO4yVoqgy8Bg09a5MnENRcJXgC0iy7EJYWP3VpYPXgCn3h352fKt3EppW_66c_ceKttpnOFTYGZn23TTeexldKTlrvP97e7Y9eh5gTV56bkXMGMTovBLJb1HXTbEOrCgN-qbjLIzCt4xs9t1mfFdCdRLOcnAT3YjBBt4KILmFLll3G11PJCjvoE8RLjjCBQ9wwZ3DAS4_v_-IQMEjUDAABa-BglOg4JnDHig4AuUu-rCzffByN4s9NzINRHyZ6ZYIXUhGFdG1NYZRy401mphSK65VbapSCm6ZKbiEWNhyoqxsW6WErCD4oPfQhuucvY8wa1oFbFQZ0ZBKSi6b1hpOgSEzpWlZPEDPxumZzoO0yvS8wR5e6F-P0LU1Sh-jjWX_1T5BV_W35WzRPx1s_QtvcGou |
| linkProvider | ISSN International Centre |
| 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=Barrier+methods+based+on+Jordan%E2%80%93Hilbert+algebras+for+stochastic+optimization+in+spin+factors&rft.jtitle=R.A.I.R.O.+Recherche+op%C3%A9rationnelle&rft.au=Alzalg%2C+Baha&rft.date=2024-01-01&rft.issn=0399-0559&rft.eissn=2804-7303&rft.volume=58&rft.issue=1&rft.spage=1011&rft.epage=1044&rft_id=info:doi/10.1051%2Fro%2F2023198&rft.externalDBID=n%2Fa&rft.externalDocID=10_1051_ro_2023198 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0399-0559&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0399-0559&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0399-0559&client=summon |