Data fitting with signomial programming compatible difference of convex functions
Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking a balance between the computational efficiency of Geometric Programming (GP) and the extensibility of more general methods for optimization. While techniques exist for fitting GP compatible mode...
Gespeichert in:
| Veröffentlicht in: | Optimization and engineering Jg. 24; H. 2; S. 973 - 987 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.06.2023
|
| Schlagworte: | |
| ISSN: | 1389-4420, 1573-2924 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking a balance between the computational efficiency of Geometric Programming (GP) and the extensibility of more general methods for optimization. While techniques exist for fitting GP compatible models to data, no models have been proposed that take advantage of the increased modeling flexibility available in SP. Here, a new Difference of Softmax Affine function is constructed by utilizing existing methods of GP compatible fitting in Difference of Convex (DC) functions. This new function class is fit to data in log–log space and becomes either a signomial or a set of signomials upon inverse transformation. Examples presented here include simple test cases in 1D and 2D, and a fit to the performance data of the NACA 24xx family of airfoils. In each case, RMS error is driven to less than 1%. |
|---|---|
| AbstractList | Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking a balance between the computational efficiency of Geometric Programming (GP) and the extensibility of more general methods for optimization. While techniques exist for fitting GP compatible models to data, no models have been proposed that take advantage of the increased modeling flexibility available in SP. Here, a new Difference of Softmax Affine function is constructed by utilizing existing methods of GP compatible fitting in Difference of Convex (DC) functions. This new function class is fit to data in log–log space and becomes either a signomial or a set of signomials upon inverse transformation. Examples presented here include simple test cases in 1D and 2D, and a fit to the performance data of the NACA 24xx family of airfoils. In each case, RMS error is driven to less than 1%. |
| Author | Karcher, Cody J. |
| Author_xml | – sequence: 1 givenname: Cody J. surname: Karcher fullname: Karcher, Cody J. email: ckarcher@mit.edu organization: Department of Aeronautics and Astronautics, Massachusetts Institute of Technology |
| BookMark | eNp9kNtKAzEQQINUsK3-gE_7A9HcdpM8Sr1CQQR9DtlssqbsJiVJvfy9W-uTD4WBGZg5w8xZgFmIwQJwidEVRohfZ4yRwBARApHkmEN2Aua45hQSSdhsqqmQkDGCzsAi5w1CuKmJmIOXW1105XwpPvTVpy_vVfZ9iKPXQ7VNsU96HPctE8etLr4dbNV552yywdgquqkRPuxX5XbBFB9DPgenTg_ZXvzlJXi7v3tdPcL188PT6mYNDaV1gdzxtmVMsqYV2CIpmprLKQjGwmrXGYoapFurZScko6ahVlArO44obwnHdAnEYa9JMedknTK-6P0JJWk_KIzUXo06qFGTGvWrRrEJJf_QbfKjTt_HIXqA8jQcepvUJu5SmF48Rv0AiqB5YQ |
| CitedBy_id | crossref_primary_10_1109_TIP_2022_3228521 |
| Cites_doi | 10.2514/6.2018-3973 10.2514/1.J052732 10.2514/1.J057020 10.2514/6.2018-0105 10.2514/6.2020-0160 10.2140/pjm.1959.9.707 10.1007/s11081-016-9332-3 10.2514/6.2016-2003 10.1007/s11081-007-9001-7 10.2514/6.2013-1532 10.2514/1.C034405 10.1007/978-3-642-84010-4_1 10.2514/1.J051895 10.2514/1.C034463 10.1002/9781118568101 10.2514/1.C034378 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2022 |
| Copyright_xml | – notice: The Author(s) 2022 |
| DBID | C6C AAYXX CITATION |
| DOI | 10.1007/s11081-022-09717-4 |
| DatabaseName | Springer Nature OA Free Journals CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1573-2924 |
| EndPage | 987 |
| ExternalDocumentID | 10_1007_s11081_022_09717_4 |
| GrantInformation_xml | – fundername: Massachusetts Institute of Technology (MIT) |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 123 1N0 1SB 203 29N 2J2 2JN 2JY 2KG 2LR 2P1 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 ABBBX ABBXA ABDZT ABECU ABFSI ABFTD ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFO ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACREN ACSNA ACZOJ ADHHG ADHIR ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADYOE ADZKW AEBTG AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFGCZ AFLOW AFQWF AFWTZ AFYQB 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 AMTXH AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ IWAJR IXC IXD IXE IZIGR IZQ I~X I~Z J-C J0Z J9A JBSCW JCJTX JZLTJ KDC KOV LAK LLZTM M4Y MA- N2Q N9A NB0 NPVJJ NQJWS NU0 O9- O93 O9J OAM OVD P2P P9R PF0 PT4 Q2X QOS R89 R9I RNI RNS ROL RPX RSV RZC RZE S16 S1Z S27 S3B SAP SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7R Z7S Z7X Z7Y Z7Z Z83 Z88 ZMTXR ~A9 8AO AAPKM AAYXX ABBRH ABDBE ABFSG ABJCF ABRTQ ACSTC ADHKG AEZWR AFDZB AFFHD AFHIU AFKRA AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA BENPR BGLVJ CCPQU CITATION HCIFZ M7S PHGZM PHGZT PQGLB PTHSS S0W |
| ID | FETCH-LOGICAL-c335t-7f7bb44946b81e09865795792118eafdc3060abea9d8943c63e83e9d7037b2713 |
| IEDL.DBID | RSV |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000779244200001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1389-4420 |
| IngestDate | Tue Nov 18 21:45:48 EST 2025 Sat Nov 29 01:39:10 EST 2025 Fri Feb 21 02:45:46 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Signomial programming Log-log convexity Difference of convex functions Data fitting |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c335t-7f7bb44946b81e09865795792118eafdc3060abea9d8943c63e83e9d7037b2713 |
| OpenAccessLink | https://link.springer.com/10.1007/s11081-022-09717-4 |
| PageCount | 15 |
| ParticipantIDs | crossref_citationtrail_10_1007_s11081_022_09717_4 crossref_primary_10_1007_s11081_022_09717_4 springer_journals_10_1007_s11081_022_09717_4 |
| PublicationCentury | 2000 |
| PublicationDate | 20230600 2023-06-00 |
| PublicationDateYYYYMMDD | 2023-06-01 |
| PublicationDate_xml | – month: 6 year: 2023 text: 20230600 |
| PublicationDecade | 2020 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationSubtitle | International Multidisciplinary Journal to Promote Optimization Theory & Applications in Engineering Sciences |
| PublicationTitle | Optimization and engineering |
| PublicationTitleAbbrev | Optim Eng |
| PublicationYear | 2023 |
| Publisher | Springer US |
| Publisher_xml | – name: Springer US |
| References | YorkMAÖztürkBBurnellEHoburgWWEfficient aircraft multidisciplinary design optimization and sensitivity analysis via signomial programmingAIAA J201856114546456110.2514/1.J057020 Hoburg W, Abbeel P (2013) Fast wind turbine design via geometric programming. In: 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, pp. 1–9. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2013-1532 HoburgWAbbeelPGeometric programming for aircraft design optimizationAIAA J201452112414242610.2514/1.J052732 BoydSKimSJVandenbergheLHassibiAA tutorial on geometric programmingOptim Eng20078167127233046710.1007/s11081-007-9001-71178.90270 Lin B, Carpenter M, de Weck O (2020) Simultaneous vehicle and trajectory design using convex optimization. In: AIAA Scitech 2020 Forum, pp. 1–18. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2020-0160 Bertsimas D (2009) 15.093J/6.255J optimization methods. Massachusetts Institute of Technology: MIT OpenCouseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA (Fall). https://ocw.mit.edu/courses/sloan-school-of-management/15-093j-optimization-methods-fall-2009/lecture-notes TorenbeekEAdvanced aircraft design: conceptual design, analysis and optimization of subsonic civil airplanes2013New YorkWiley10.1002/9781118568101 YorkMAHoburgWWDrelaMTurbofan engine sizing and tradeoff analysis via signomial programmingJ Aircraft2018553988100310.2514/1.C034463 Kirschen PG, Burnell E, Hoburg W (2016) Signomial programming models for aircraft design. In: 54th AIAA Aerospace Sciences Meeting, pp. 1–26. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2016-2003 Saab A, Burnell E, Hoburg WW (2018) Robust designs via geometric programming. arXiv. https://arxiv.org/abs/1808.07192 HartmanPOn functions representable as a difference of convex functionsPac J Math19599370771311077310.2140/pjm.1959.9.7070093.06401 KirschenPGYorkMAOzturkBHoburgWWApplication of signomial programming to aircraft designJ Aircraft201855396598710.2514/1.C034378 DrelaMDrelaMMuellerTJXfoil: an analysis and design system for low Reynolds number airfoilsLow Reynolds number aerodynamics1989BerlinSpringer11210.1007/978-3-642-84010-4_1 HoburgWKirschenPAbbeelPData fitting with geometric-programming-compatible softmax functionsOptim Eng2016174897918357127310.1007/s11081-016-9332-31364.65120 Hall DK, Dowdle A, Gonzalez J, Trollinger L, Thalheimer W (2018) Assessment of a boundary layer ingesting turboelectric aircraft configuration using signomial programming. In: 2018 aviation technology, integration, and operations conference, pp. 1–16. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2018-3973 MartinsJRRALambeABMultidisciplinary design optimization: a survey of architecturesAIAA J20135192049207510.2514/1.J051895 BurtonMHoburgWSolar and gas powered long-endurance unmanned aircraft sizing via geometric programmingJ Aircraft201855121222510.2514/1.C034405 Brown A, Harris W (2018) A vehicle design and optimization model for on-demand aviation. In: 2018 AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference, pp. 1–46. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2018-0105 Opgenoord MMJ, Cohen BS, Hoburg WW (2017) Comparison of algorithms for including equality constraints in signomial programming. Technical Report ACDL TR-2017-1, Massachusetts Institute of Technology. https://convex.mit.edu/publications/SignomialEquality.pdf M Burton (9717_CR4) 2018; 55 W Hoburg (9717_CR10) 2016; 17 9717_CR3 9717_CR8 9717_CR6 M Drela (9717_CR5) 1989 JRRA Martins (9717_CR14) 2013; 51 E Torenbeek (9717_CR17) 2013 9717_CR11 9717_CR16 MA York (9717_CR19) 2018; 56 9717_CR1 9717_CR15 9717_CR13 P Hartman (9717_CR7) 1959; 9 PG Kirschen (9717_CR12) 2018; 55 MA York (9717_CR18) 2018; 55 S Boyd (9717_CR2) 2007; 8 W Hoburg (9717_CR9) 2014; 52 |
| References_xml | – reference: YorkMAHoburgWWDrelaMTurbofan engine sizing and tradeoff analysis via signomial programmingJ Aircraft2018553988100310.2514/1.C034463 – reference: BoydSKimSJVandenbergheLHassibiAA tutorial on geometric programmingOptim Eng20078167127233046710.1007/s11081-007-9001-71178.90270 – reference: Brown A, Harris W (2018) A vehicle design and optimization model for on-demand aviation. In: 2018 AIAA/ASCE/AHS/ASC structures, structural dynamics, and materials conference, pp. 1–46. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2018-0105 – reference: Hall DK, Dowdle A, Gonzalez J, Trollinger L, Thalheimer W (2018) Assessment of a boundary layer ingesting turboelectric aircraft configuration using signomial programming. In: 2018 aviation technology, integration, and operations conference, pp. 1–16. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2018-3973 – reference: MartinsJRRALambeABMultidisciplinary design optimization: a survey of architecturesAIAA J20135192049207510.2514/1.J051895 – reference: YorkMAÖztürkBBurnellEHoburgWWEfficient aircraft multidisciplinary design optimization and sensitivity analysis via signomial programmingAIAA J201856114546456110.2514/1.J057020 – reference: HoburgWAbbeelPGeometric programming for aircraft design optimizationAIAA J201452112414242610.2514/1.J052732 – reference: Lin B, Carpenter M, de Weck O (2020) Simultaneous vehicle and trajectory design using convex optimization. In: AIAA Scitech 2020 Forum, pp. 1–18. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2020-0160 – reference: TorenbeekEAdvanced aircraft design: conceptual design, analysis and optimization of subsonic civil airplanes2013New YorkWiley10.1002/9781118568101 – reference: DrelaMDrelaMMuellerTJXfoil: an analysis and design system for low Reynolds number airfoilsLow Reynolds number aerodynamics1989BerlinSpringer11210.1007/978-3-642-84010-4_1 – reference: HoburgWKirschenPAbbeelPData fitting with geometric-programming-compatible softmax functionsOptim Eng2016174897918357127310.1007/s11081-016-9332-31364.65120 – reference: Bertsimas D (2009) 15.093J/6.255J optimization methods. Massachusetts Institute of Technology: MIT OpenCouseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA (Fall). https://ocw.mit.edu/courses/sloan-school-of-management/15-093j-optimization-methods-fall-2009/lecture-notes/ – reference: KirschenPGYorkMAOzturkBHoburgWWApplication of signomial programming to aircraft designJ Aircraft201855396598710.2514/1.C034378 – reference: Saab A, Burnell E, Hoburg WW (2018) Robust designs via geometric programming. arXiv. https://arxiv.org/abs/1808.07192 – reference: Hoburg W, Abbeel P (2013) Fast wind turbine design via geometric programming. In: 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, pp. 1–9. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2013-1532 – reference: Kirschen PG, Burnell E, Hoburg W (2016) Signomial programming models for aircraft design. In: 54th AIAA Aerospace Sciences Meeting, pp. 1–26. American Institute of Aeronautics and Astronautics, Reston. https://doi.org/10.2514/6.2016-2003 – reference: BurtonMHoburgWSolar and gas powered long-endurance unmanned aircraft sizing via geometric programmingJ Aircraft201855121222510.2514/1.C034405 – reference: Opgenoord MMJ, Cohen BS, Hoburg WW (2017) Comparison of algorithms for including equality constraints in signomial programming. Technical Report ACDL TR-2017-1, Massachusetts Institute of Technology. https://convex.mit.edu/publications/SignomialEquality.pdf – reference: HartmanPOn functions representable as a difference of convex functionsPac J Math19599370771311077310.2140/pjm.1959.9.7070093.06401 – ident: 9717_CR6 doi: 10.2514/6.2018-3973 – volume: 52 start-page: 2414 issue: 11 year: 2014 ident: 9717_CR9 publication-title: AIAA J doi: 10.2514/1.J052732 – volume: 56 start-page: 4546 issue: 11 year: 2018 ident: 9717_CR19 publication-title: AIAA J doi: 10.2514/1.J057020 – ident: 9717_CR15 – ident: 9717_CR3 doi: 10.2514/6.2018-0105 – ident: 9717_CR16 – ident: 9717_CR13 doi: 10.2514/6.2020-0160 – volume: 9 start-page: 707 issue: 3 year: 1959 ident: 9717_CR7 publication-title: Pac J Math doi: 10.2140/pjm.1959.9.707 – volume: 17 start-page: 897 issue: 4 year: 2016 ident: 9717_CR10 publication-title: Optim Eng doi: 10.1007/s11081-016-9332-3 – ident: 9717_CR11 doi: 10.2514/6.2016-2003 – ident: 9717_CR1 – volume: 8 start-page: 67 issue: 1 year: 2007 ident: 9717_CR2 publication-title: Optim Eng doi: 10.1007/s11081-007-9001-7 – ident: 9717_CR8 doi: 10.2514/6.2013-1532 – volume: 55 start-page: 212 issue: 1 year: 2018 ident: 9717_CR4 publication-title: J Aircraft doi: 10.2514/1.C034405 – start-page: 1 volume-title: Low Reynolds number aerodynamics year: 1989 ident: 9717_CR5 doi: 10.1007/978-3-642-84010-4_1 – volume: 51 start-page: 2049 issue: 9 year: 2013 ident: 9717_CR14 publication-title: AIAA J doi: 10.2514/1.J051895 – volume: 55 start-page: 988 issue: 3 year: 2018 ident: 9717_CR18 publication-title: J Aircraft doi: 10.2514/1.C034463 – volume-title: Advanced aircraft design: conceptual design, analysis and optimization of subsonic civil airplanes year: 2013 ident: 9717_CR17 doi: 10.1002/9781118568101 – volume: 55 start-page: 965 issue: 3 year: 2018 ident: 9717_CR12 publication-title: J Aircraft doi: 10.2514/1.C034378 |
| SSID | ssj0016528 |
| Score | 2.2949705 |
| Snippet | Signomial Programming (SP) has proven to be a powerful tool for engineering design optimization, striking a balance between the computational efficiency of... |
| SourceID | crossref springer |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 973 |
| SubjectTerms | Control Engineering Environmental Management Financial Engineering Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Research Article Systems Theory |
| Title | Data fitting with signomial programming compatible difference of convex functions |
| URI | https://link.springer.com/article/10.1007/s11081-022-09717-4 |
| Volume | 24 |
| WOSCitedRecordID | wos000779244200001&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: 1573-2924 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0016528 issn: 1389-4420 databaseCode: RSV dateStart: 20000601 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/eLvHCXMwnV1LS8QwEB509aAH3-L6IgdvGugjbZKjqIsXF8UHeytJmsLCPmRbxZ9vJtvuuiALeixNS5lMZzqdb74P4CLSeaRDrlxtog1lVuRUCx24YFi49KaMDfOp2ATvdkWvJx_robCyQbs3LUkfqefDbqFLXxTR58h7xClbhbUE2WawRn9-m_UO0sQrqmIHjjIWBfWozO_3WExHi71Qn2I62_97uB3Yqj8pyfXUB3ZhxY72YPMH0aA7epixs5b78HSrKkWKvoc8E_wTSxDGMR46XyQ1YGuIpzxAverrgSWNkIqxZFwQj1X_IpgUvd8ewGvn7uXmntbSCtTEcVJRXnCtGZMs1SK0gRRpwrFh58pBYVWRG1dJBEpbJXMkaDdpbEVsZe7iA9eRK2wPoTUaj-wRkDjXtpDITB8appBvT_IiVYaJyARayTaEjYUzU_OOo_zFIJszJqPxMme8zBsvY224nF3zPmXdWLr6qtmUrH4DyyXLj_-2_AQ2UGJ-Cg87hVY1-bBnsG4-q345Ofeu9w0IQtI2 |
| linkProvider | Springer Nature |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1bS8MwFD7oFNQH7-K85sE3DfSSNcmjqGPiNhSn7K0kaQqDXWSt4s83SdvNgQj6WJqWcnJ6Tk_Pd74P4CKQSSB9KkxtIhUmmiVYMumZYJia9CaU9pNCbIJ2u6zf54_lUFhWod2rlqSL1PNhN9-kL2zR55b3iGKyDCvEyuzYGv35ddY7iBpOUdV24DAhgVeOyvx8j8V0tNgLdSmmufW_h9uGzfKTEl0XPrADS3q8CxvfiAbNUWfGzprtwdOtyAVKBw7yjOyfWGRhHJOR8UVUArZG9pQDqOcDOdSoElJRGk1S5LDqn8gmRee3-_DSvOvdtHAprYBVGDZyTFMqJSGcRJL52uMsalDbsDPlINMiTZSpJDwhteCJJWhXUahZqHli4gOVgSlsD6A2noz1IaAwkTrllpneV0RYvj1O00gowgLlScHr4FcWjlXJO27lL4bxnDHZGi82xoud8WJSh8vZNW8F68avq6-qTYnLNzD7ZfnR35afw1qr12nH7fvuwzGsW7n5Aip2ArV8-q5PYVV95INseubc8AvsPNUa |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1ZS8NAEF60iuiDt1jPffBNl-bYZrOPYi2KWupJ38KeUGjT0kbx57u7SXqAFMTHkEkIs5OdTOab7wPgIuAy4D5hpjbhAmEVS8Rj7pnNUJv0xoTyZS42QVqtuNOh7Zkpfod2L1uS-UyDZWlKs9pQ6tp08M03qQxZJLrlQCIIL4MVbCoZC-p6ef2Y9BGiulNXtd04hHHgFWMzv99jPjXN90Vdumlu_f9Bt8Fm8akJr_PY2AFLKt0FGzMEhOboacLaOt4Dzw2WMai7DgoN7R9aaOEdg76JUVgAufr2lAOuZ13eU7AUWBEKDjR0GPZvaJOli-d98N68fbu5Q4XkAhJhWM8Q0YRzjCmOeOwrj8ZRndhGnikTY8W0FKbC8BhXjEpL3C6iUMWhotLsG4QHpuA9AJV0kKpDAEPJlaaWsd4XmFkePkp0xASOA-FxRqvAL72diIKP3Mpi9JIpk7J1XmKclzjnJbgKLifXDHM2joXWV-UCJcWbOV5gfvQ383Ow1m40k8f71sMxWLcq9DmC7ARUstGnOgWr4ivrjkdnLiJ_AEyM3f4 |
| 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=Data+fitting+with+signomial+programming+compatible+difference+of+convex+functions&rft.jtitle=Optimization+and+engineering&rft.au=Karcher%2C+Cody+J.&rft.date=2023-06-01&rft.issn=1389-4420&rft.eissn=1573-2924&rft.volume=24&rft.issue=2&rft.spage=973&rft.epage=987&rft_id=info:doi/10.1007%2Fs11081-022-09717-4&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11081_022_09717_4 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1389-4420&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1389-4420&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1389-4420&client=summon |