A polynomial-time algorithm for a nonconvex chance-constrained program under the normal approximation
We study a chance-constrained optimization problem where the random variable appearing in the chance constraint follows a normal distribution whose mean and variance both depend linearly on the decision variables. Such structure may arise in many applications, including the normal approximation to t...
Uloženo v:
| Vydáno v: | Optimization letters Ročník 17; číslo 2; s. 265 - 282 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.03.2023
|
| Témata: | |
| ISSN: | 1862-4472, 1862-4480 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | We study a chance-constrained optimization problem where the random variable appearing in the chance constraint follows a normal distribution whose mean and variance both depend linearly on the decision variables. Such structure may arise in many applications, including the normal approximation to the Poisson distribution. We present a polynomial-time algorithm to solve the resulting nonconvex optimization problem, and illustrate the efficacy of our method using a numerical experiment. |
|---|---|
| AbstractList | We study a chance-constrained optimization problem where the random variable appearing in the chance constraint follows a normal distribution whose mean and variance both depend linearly on the decision variables. Such structure may arise in many applications, including the normal approximation to the Poisson distribution. We present a polynomial-time algorithm to solve the resulting nonconvex optimization problem, and illustrate the efficacy of our method using a numerical experiment. |
| Author | Mildebrath, David |
| Author_xml | – sequence: 1 givenname: David surname: Mildebrath fullname: Mildebrath, David email: dtm3@rice.edu organization: Department of Computational and Applied Mathematics, Rice University |
| BookMark | eNp9kMtOwzAQRS1UJErhB1j5Bwx-JE68rCpeUiU2sLYmU6dNldiRnaL27zEUsWQ1M5p7Z67ONZn54B0hd4LfC86rhyREaTjjUjIuDC-ZviBzUWvJiqLms7--klfkOqU951oIY-bELekY-pMPQwc9m7rBUei3IXbTbqBtiBRofoXBf7ojxR14dCxPaYrQebehYwzbCAM9-I2LdNq5LI8D9BTGvDp2A0xd8DfksoU-udvfuiAfT4_vqxe2fnt-XS3XDGUhJ1bJSooadYugsSmV4uVGATatc4VpDIIU2mBZAm-kzm1Tq6ZQaIxElKo1akHk-S7GkFJ0rR1jjhBPVnD7DcqeQdkMyv6Asjqb1NmUsthvXbT7cIg-5_zP9QW6i2_b |
| Cites_doi | 10.1007/BF00938217 10.1007/978-94-017-3087-7 10.1007/BF01442883 10.1007/BF01442898 10.1287/ijoc.1120.0530 10.1007/BF02283685 10.1016/j.trb.2017.05.014 10.1016/j.orl.2010.01.003 10.1016/0167-6377(83)90038-X 10.1287/mnsc.4.3.235 10.1017/CBO9780511804441 10.1287/ijoc.2014.0595 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s11590-022-01905-6 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1862-4480 |
| EndPage | 282 |
| ExternalDocumentID | 10_1007_s11590_022_01905_6 |
| GrantInformation_xml | – fundername: National Defense Science and Engineering Graduate funderid: http://dx.doi.org/10.13039/100014037 |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .VR 06D 0R~ 0VY 123 1N0 203 2J2 2JN 2JY 2KG 2KM 2LR 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBXA ABDZT ABECU ABFTV ABHQN ABJNI ABJOX ABKCH ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ AXYYD AYJHY B-. BA0 BAPOH BDATZ BGNMA BSONS CAG COF CS3 CSCUP DDRTE DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HLICF HMJXF HQYDN HRMNR HZ~ IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ KDC KOV LLZTM M4Y MA- N9A NPVJJ NQJWS NU0 O9- O93 O9J OAM P2P P9M PF0 PT4 QOS R89 R9I ROL RPX RSV S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7Y Z83 Z88 ZMTXR ~A9 AAPKM AAYXX ABBRH ABDBE ABFSG ABRTQ ACSTC AEZWR AFDZB AFHIU AFOHR AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION |
| ID | FETCH-LOGICAL-c242t-727218c6fca6cb53305d3acbfee49b9ca2169c55a0b26169b83b43c992cc23f93 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000825924400001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1862-4472 |
| IngestDate | Sat Nov 29 02:44:13 EST 2025 Fri Feb 21 02:45:00 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Reverse convex programming Chance-constrained programming Polynomial-time algorithms Nonlinear optimization |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c242t-727218c6fca6cb53305d3acbfee49b9ca2169c55a0b26169b83b43c992cc23f93 |
| PageCount | 18 |
| ParticipantIDs | crossref_primary_10_1007_s11590_022_01905_6 springer_journals_10_1007_s11590_022_01905_6 |
| PublicationCentury | 2000 |
| PublicationDate | 20230300 2023-03-00 |
| PublicationDateYYYYMMDD | 2023-03-01 |
| PublicationDate_xml | – month: 3 year: 2023 text: 20230300 |
| PublicationDecade | 2020 |
| PublicationPlace | Berlin/Heidelberg |
| PublicationPlace_xml | – name: Berlin/Heidelberg |
| PublicationTitle | Optimization letters |
| PublicationTitleAbbrev | Optim Lett |
| PublicationYear | 2023 |
| Publisher | Springer Berlin Heidelberg |
| Publisher_xml | – name: Springer Berlin Heidelberg |
| References | GoyalVRaviRA PTAS for the chance-constrained knapsack problem with random item sizesOper. Res. Lett.201038161164260885010.1016/j.orl.2010.01.0031187.90232 BoydSVandenbergheLConvex Optimization2004CambridgeCambridge University Press10.1017/CBO97805118044411058.90049 ChenJChenLSunDAir traffic flow management under uncertainty using chance-constrained optimizationTransport. Res. Part B Methodol.201710212414110.1016/j.trb.2017.05.014 HillestadRJJacobsenSELinear programs with an additional reverse convex constraintAppl. Math. Optim.19806125726957626310.1007/BF014428980435.90065 PrèkopaAStochastic Programming. Mathematics and Its Applications1995DordrechtKluwer Academic Publishers0863.90116 HillestadRJJacobsenSEReverse convex programmingAppl. Math. Optim.198061637855705510.1007/BF014428830448.90044 NocedalJWrightSJNumerical Optimization20062New YorkSpringer1104.65059 KatohNIbarakiTA polynomial time algorithm for a chance-constrained single machine scheduling problemOper. Res. Lett.198322626571557210.1016/0167-6377(83)90038-X0506.90039 CharnesACooperWWSymondsGHCost horizons and certainty equivalents: an approach to stochastic programming of heating oilManag. Sci.19584323526310.1287/mnsc.4.3.235 SongYLuedtkeJRKüçükyavuzSChance-constrained binary packing problemsINFORMS J. Comput.2014264735747326580410.1287/ijoc.2014.05951304.90179 TuyHConvex programs with an additional reverse convex constraintJ. Optim. Theory Appl.198752346348688099610.1007/BF009382170585.90071 ShyloOVProkopyevOASchaeferAJStochastic operating room scheduling for high-volume specialties under block bookingINFORMS J. Comput.2013254682692312092710.1287/ijoc.1120.0530 Mildebrath, D., Lee, T., Sinha, S., Schaefer, A.J., Gaber, A.O.: Characterizing rational transplant program response to outcome-based regulation. Oper. Res., To appear (2021) SaadSBJacobsenSEA level set algorithm for a class of reverse convex programsAnn. Oper. Res.1990251942108442110.1007/BF022836850714.90078 V Goyal (1905_CR6) 2010; 38 RJ Hillestad (1905_CR11) 1980; 6 A Prèkopa (1905_CR1) 1995 1905_CR5 N Katoh (1905_CR9) 1983; 2 SB Saad (1905_CR13) 1990; 25 J Nocedal (1905_CR14) 2006 H Tuy (1905_CR12) 1987; 52 J Chen (1905_CR8) 2017; 102 S Boyd (1905_CR3) 2004 Y Song (1905_CR7) 2014; 26 RJ Hillestad (1905_CR10) 1980; 6 OV Shylo (1905_CR4) 2013; 25 A Charnes (1905_CR2) 1958; 4 |
| References_xml | – reference: HillestadRJJacobsenSEReverse convex programmingAppl. Math. Optim.198061637855705510.1007/BF014428830448.90044 – reference: BoydSVandenbergheLConvex Optimization2004CambridgeCambridge University Press10.1017/CBO97805118044411058.90049 – reference: TuyHConvex programs with an additional reverse convex constraintJ. Optim. Theory Appl.198752346348688099610.1007/BF009382170585.90071 – reference: KatohNIbarakiTA polynomial time algorithm for a chance-constrained single machine scheduling problemOper. Res. Lett.198322626571557210.1016/0167-6377(83)90038-X0506.90039 – reference: GoyalVRaviRA PTAS for the chance-constrained knapsack problem with random item sizesOper. Res. Lett.201038161164260885010.1016/j.orl.2010.01.0031187.90232 – reference: SongYLuedtkeJRKüçükyavuzSChance-constrained binary packing problemsINFORMS J. Comput.2014264735747326580410.1287/ijoc.2014.05951304.90179 – reference: PrèkopaAStochastic Programming. Mathematics and Its Applications1995DordrechtKluwer Academic Publishers0863.90116 – reference: ChenJChenLSunDAir traffic flow management under uncertainty using chance-constrained optimizationTransport. Res. Part B Methodol.201710212414110.1016/j.trb.2017.05.014 – reference: NocedalJWrightSJNumerical Optimization20062New YorkSpringer1104.65059 – reference: CharnesACooperWWSymondsGHCost horizons and certainty equivalents: an approach to stochastic programming of heating oilManag. Sci.19584323526310.1287/mnsc.4.3.235 – reference: ShyloOVProkopyevOASchaeferAJStochastic operating room scheduling for high-volume specialties under block bookingINFORMS J. Comput.2013254682692312092710.1287/ijoc.1120.0530 – reference: Mildebrath, D., Lee, T., Sinha, S., Schaefer, A.J., Gaber, A.O.: Characterizing rational transplant program response to outcome-based regulation. Oper. Res., To appear (2021) – reference: SaadSBJacobsenSEA level set algorithm for a class of reverse convex programsAnn. Oper. Res.1990251942108442110.1007/BF022836850714.90078 – reference: HillestadRJJacobsenSELinear programs with an additional reverse convex constraintAppl. Math. Optim.19806125726957626310.1007/BF014428980435.90065 – volume: 52 start-page: 463 issue: 3 year: 1987 ident: 1905_CR12 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00938217 – volume-title: Stochastic Programming. Mathematics and Its Applications year: 1995 ident: 1905_CR1 doi: 10.1007/978-94-017-3087-7 – volume: 6 start-page: 63 issue: 1 year: 1980 ident: 1905_CR11 publication-title: Appl. Math. Optim. doi: 10.1007/BF01442883 – ident: 1905_CR5 – volume: 6 start-page: 257 issue: 1 year: 1980 ident: 1905_CR10 publication-title: Appl. Math. Optim. doi: 10.1007/BF01442898 – volume: 25 start-page: 682 issue: 4 year: 2013 ident: 1905_CR4 publication-title: INFORMS J. Comput. doi: 10.1287/ijoc.1120.0530 – volume: 25 start-page: 19 year: 1990 ident: 1905_CR13 publication-title: Ann. Oper. Res. doi: 10.1007/BF02283685 – volume-title: Numerical Optimization year: 2006 ident: 1905_CR14 – volume: 102 start-page: 124 year: 2017 ident: 1905_CR8 publication-title: Transport. Res. Part B Methodol. doi: 10.1016/j.trb.2017.05.014 – volume: 38 start-page: 161 year: 2010 ident: 1905_CR6 publication-title: Oper. Res. Lett. doi: 10.1016/j.orl.2010.01.003 – volume: 2 start-page: 62 issue: 2 year: 1983 ident: 1905_CR9 publication-title: Oper. Res. Lett. doi: 10.1016/0167-6377(83)90038-X – volume: 4 start-page: 235 issue: 3 year: 1958 ident: 1905_CR2 publication-title: Manag. Sci. doi: 10.1287/mnsc.4.3.235 – volume-title: Convex Optimization year: 2004 ident: 1905_CR3 doi: 10.1017/CBO9780511804441 – volume: 26 start-page: 735 issue: 4 year: 2014 ident: 1905_CR7 publication-title: INFORMS J. Comput. doi: 10.1287/ijoc.2014.0595 |
| SSID | ssj0061199 |
| Score | 2.2744052 |
| Snippet | We study a chance-constrained optimization problem where the random variable appearing in the chance constraint follows a normal distribution whose mean and... |
| SourceID | crossref springer |
| SourceType | Index Database Publisher |
| StartPage | 265 |
| SubjectTerms | Computational Intelligence Mathematics Mathematics and Statistics Numerical and Computational Physics Operations Research/Decision Theory Optimization Original Paper Simulation |
| Title | A polynomial-time algorithm for a nonconvex chance-constrained program under the normal approximation |
| URI | https://link.springer.com/article/10.1007/s11590-022-01905-6 |
| Volume | 17 |
| WOSCitedRecordID | wos000825924400001&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: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1862-4480 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0061199 issn: 1862-4472 databaseCode: RSV dateStart: 20070101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8QwEA66etCDb3F9kYM3DbTNY5PjIooXF8EHeytJmupC3V3aKuu_N9OH64IIeiwMIUzSmQnzffMhdJb4lMGlSgAlTgnTjBLDnSLCUi2NS30ODiqxid5gIIdDddeQwooW7d62JKtIPSe7-cwbEECfA_-ZE7GMVjhMm4E3-v1TG39FWKtGhhL4QKwXNVSZn9dYTEeLvdAqxVxv_m9zW2ijKSlxv74D22jJjXfQ-rdBg_7r9ms6a7GLXB9PJ9kHEJJ1RkBdHuvseZKPypdX7ItYrPF4Mq7w6DMMzGDriIU6EuQkXIIbTBcG_lmO_cLe3Mf3DFcDymejmg25hx6vrx4ub0gjt0Csz9MlgZZsKK1IrRbWAOqUJ1RbkzrHlFFWR6FQlnMdGP_sEspIahi1SkXWRjRVdB91_O7cAcI20Jb6c0glYyxJpXZGO8782TvBTRB10Xnr9XhaT9WI5_OTwZWxd2VcuTIWXXTROj1u_rDiF_PDv5kfoTWQkK9xZceoU-Zv7gSt2vdyVOSn1dX6BMsfykc |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LSwMxEA5aBfXgW6zPHLxpYHfzaHIsYqnYFsEqvS1JNquF2pbdVeq_N9mHtSCCHheGECbZmQnzffMBcBHZlEG5iBxKHCMiCUaKGoGYxpIrE9sc7OViE41ejw8G4r4khaUV2r1qSeaRek52s5nXQw597vjPFLFlsEKczI57oz88VfGX-YVqpM8dH4g0gpIq8_Mai-losReap5jW1v82tw02y5ISNos7sAOWzHgXbHwbNGi_ul_TWdM9YJpwOhl9OEKyHCGnLg_l6HmSDLOXV2iLWCjheDLO8egz6JjB2iDt6kgnJ2EiWGK6oOOfJdAubM1tfB_BfED5bFiwIffBY-umf91GpdwC0jZPZ8i1ZH2uWawl08qhTmmEpVaxMUQooWXgM6EplZ6yzy4mFMeKYC1EoHWAY4EPQM3uzhwCqD2psT2HmBNCophLo6ShxJ69YVR5QR1cVl4Pp8VUjXA-P9m5MrSuDHNXhqwOriqnh-Uflv5ifvQ383Ow1u53O2Hntnd3DNadnHyBMTsBtSx5M6dgVb9nwzQ5y6_ZJ1DYzSs |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1bS8MwFA46RfTBuzivefBNw9rmsuZxqENRx_DG3kqSpjqo3eiqzH9v0ovbQATxsXAI4Zw054TzfecD4CQ0KYP6PLQocYyIIBhJqjliCgtf6sjkYCcXm2h2On6vx7tTLP4c7V61JAtOg53SlGSNYRg1JsQ3k4UdZJHolgtNEZsHC8S8ZCyo6_7hubqLmVsoSLq-5QaRplfSZn5eYzY1zfZF83TTXvv_RtfBallqwlZxNjbAnE42wcrUAELzdfc9tXW0BXQLDgfxpyUqixhZ1Xko4pdB2s9e36ApbqGAySDJcepjaBnDSiNl60srM6FDWGK9oOWlpdAsbMzNvR_DfHD5uF-wJLfBU_vy8fwKlTIMSJn8nSHbqnV9xSIlmJIWjUpDLJSMtCZcciU8l3FFqXCkeY4xLn0sCVace0p5OOJ4B9TM7vQugMoRCpuYRD4hJIx8oaXQlJgzoRmVjlcHp1UEgmExbSOYzFW2rgyMK4PclQGrg7MqAEH5541-Md_7m_kxWOpetIPb687NPli2KvMF9OwA1LL0XR-CRfWR9UfpUX7ivgB88tYP |
| 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+polynomial-time+algorithm+for+a+nonconvex+chance-constrained+program+under+the+normal+approximation&rft.jtitle=Optimization+letters&rft.au=Mildebrath%2C+David&rft.date=2023-03-01&rft.issn=1862-4472&rft.eissn=1862-4480&rft.volume=17&rft.issue=2&rft.spage=265&rft.epage=282&rft_id=info:doi/10.1007%2Fs11590-022-01905-6&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11590_022_01905_6 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1862-4472&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1862-4472&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1862-4472&client=summon |