First and second order necessary optimality conditions for multiobjective programming with interval-valued objective functions on Riemannian manifolds
The growing dependence on optimization models in decision-making has created a demand for tools that can facilitate the formulation and resolution of a broader range of real-world processes and systems associated with human activity. These situations often involve assumptions that diverge from tradi...
Uloženo v:
| Vydáno v: | R.A.I.R.O. Recherche opérationnelle Ročník 58; číslo 5; s. 4259 - 4276 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
01.09.2024
|
| ISSN: | 0399-0559, 2804-7303 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | The growing dependence on optimization models in decision-making has created a demand for tools that can facilitate the formulation and resolution of a broader range of real-world processes and systems associated with human activity. These situations often involve assumptions that diverge from traditional optimization methodologies. One viable approach for addressing optimization problems in real-life scenarios with uncertainty is interval-valued optimization. Taking into account the significance of interval-valued optimization, in this paper, we derive first and second order necessary optimality conditions for a multi-objective programming problem with interval-valued objective functions defined on a Riemannian manifold. To establish these conditions, we consider the objective functions to be weakly differentiable and twice weakly differentiable for first and second order, respectively. Additionally, we assume that the constraints, both equality and inequality constraints, are differentiable and twice differentiable for first and second order conditions respectively. The first order as well as second order necessary conditions are derived under two types of constraint qualifications. Furthermore, we provide illustrative examples to demonstrate the application of the established results. |
|---|---|
| AbstractList | The growing dependence on optimization models in decision-making has created a demand for tools that can facilitate the formulation and resolution of a broader range of real-world processes and systems associated with human activity. These situations often involve assumptions that diverge from traditional optimization methodologies. One viable approach for addressing optimization problems in real-life scenarios with uncertainty is interval-valued optimization. Taking into account the significance of interval-valued optimization, in this paper, we derive first and second order necessary optimality conditions for a multi-objective programming problem with interval-valued objective functions defined on a Riemannian manifold. To establish these conditions, we consider the objective functions to be weakly differentiable and twice weakly differentiable for first and second order, respectively. Additionally, we assume that the constraints, both equality and inequality constraints, are differentiable and twice differentiable for first and second order conditions respectively. The first order as well as second order necessary conditions are derived under two types of constraint qualifications. Furthermore, we provide illustrative examples to demonstrate the application of the established results. |
| Author | Iqbal, Akhlad Aftab, Mahwash Bhat, Hilal Ahmad |
| Author_xml | – sequence: 1 givenname: Hilal Ahmad orcidid: 0000-0002-8712-3905 surname: Bhat fullname: Bhat, Hilal Ahmad – sequence: 2 givenname: Akhlad orcidid: 0000-0003-1932-2782 surname: Iqbal fullname: Iqbal, Akhlad – sequence: 3 givenname: Mahwash orcidid: 0009-0008-0561-9079 surname: Aftab fullname: Aftab, Mahwash |
| BookMark | eNo9kM1KAzEUhYNUsNZufIKshbHJJJmfpRRrhYIguh6SzE2NzCQlSSt9EZ_XlBYXl8PlHA585xZNnHeA0D0lj5QIugh-UZKSU1FfoWnZEF7UjLAJmhLWtgURor1B8xityuGmqloipuh3ZUNMWLoeR9A-iw89BOxAQ4wyHLHfJTvKwaYjPvk2We8iNj7gcT_kR32DTvYAeBf8NshxtG6Lf2z6wtYlCAc5FPn2kJv_o2bv9LnHO_xuYZTOWelwVmv80Mc7dG3kEGF-0Rn6XD1_LNfF5u3ldfm0KXRZVqloVV2ZzNGYuiLG9JJoIlTfcMWl0jJzaiVawxmnlZIUGmANMYqVuhGUm5rN0MO5VwcfYwDT7UKmDceOku40ahd8dxmV_QGKtXFu |
| Cites_doi | 10.1023/A:1006579214413 10.1080/02331934.2020.1810248 10.1137/1.9781611970906 10.1007/BF00940467 10.1007/s10957-010-9688-z 10.1017/9781009166164 10.1016/0377-2217(90)90375-L 10.1007/978-1-4615-6357-0 10.1007/s10957-011-9921-4 10.1016/j.ejor.2016.03.042 10.1515/9781400830244 10.1080/01630569108816425 10.1007/s10898-003-3780-y 10.1287/moor.2021.1203 10.1016/j.cie.2020.106634 10.1016/j.jmaa.2007.05.023 10.1137/S0363012996311095 10.1080/02331934.2012.745531 10.1007/978-94-015-8390-9_3 10.1137/18M121040X 10.1051/ro:2000122 10.1137/23M1582382 10.1090/mmono/149 10.1080/00036811.2023.2232795 10.1007/s10700-013-9156-y 10.1137/0115056 10.1137/17M1147330 10.1137/09075367X 10.1016/j.ejor.2008.03.012 10.1016/j.ejor.2005.09.007 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION |
| DOI | 10.1051/ro/2024157 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 2804-7303 |
| EndPage | 4276 |
| ExternalDocumentID | 10_1051_ro_2024157 |
| 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-9b76f9058f760ffda0c05bd84b4abca051cb59f43416ba1e8e380fb32c8514f73 |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001335541500004&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 04:47:33 EST 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 5 |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c226t-9b76f9058f760ffda0c05bd84b4abca051cb59f43416ba1e8e380fb32c8514f73 |
| ORCID | 0000-0003-1932-2782 0009-0008-0561-9079 0000-0002-8712-3905 |
| OpenAccessLink | https://doi.org/10.1051/ro/2024157 |
| PageCount | 18 |
| ParticipantIDs | crossref_primary_10_1051_ro_2024157 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-09-01 |
| PublicationDateYYYYMMDD | 2024-09-01 |
| PublicationDate_xml | – month: 09 year: 2024 text: 2024-09-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | R.A.I.R.O. Recherche opérationnelle |
| PublicationYear | 2024 |
| References | Wang (R35) 1991; 12 Andreani (R5) 2022; 3 Wu (R39) 2009; 196 Wu (R38) 2008; 338 Ishibuchi (R20) 1990; 48 Ferreira (R18) 2005; 31 Andreani (R4) 2019; 4 Rahman (R27) 2020; 147 R22 R25 R24 Wang (R36) 2010; 146 Chalco-Cano (R16) 2013; 12 McCormick (R23) 1967; 15 R29 Wu (R37) 2007; 176 Bento (R10) 2015; 64 R1 R2 Yang (R40) 2014; 10 Antczak (R7) 2022; 84 Singh (R32) 2016; 254 Rapcsak (R28) 1991; 69 Singh (R31) 2014; 5 Gabriel (R19) 2018; 22 Li (R21) 2011; 21 Penot (R26) 1998; 37 R30 Andreani (R6) 2024; 34 Bigi (R14) 2000; 34 R12 Chen (R17) 2020; 71 Szilagyi (R33) 1998; 81 R34 R11 Bento (R9) 2012; 152 R13 R15 Andreani (R3) 2019; 29 Antczak (R8) 2023; 103 |
| References_xml | – ident: R13 – volume: 81 start-page: 125 year: 1998 ident: R33 publication-title: Acta Math. Hungar. doi: 10.1023/A:1006579214413 – volume: 71 start-page: 613 year: 2020 ident: R17 publication-title: Optimization doi: 10.1080/02331934.2020.1810248 – ident: R25 doi: 10.1137/1.9781611970906 – volume: 69 start-page: 169 year: 1991 ident: R28 publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00940467 – volume: 146 start-page: 691 year: 2010 ident: R36 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-010-9688-z – ident: R15 doi: 10.1017/9781009166164 – volume: 48 start-page: 219 year: 1990 ident: R20 publication-title: Eur. J. Oper. Res. doi: 10.1016/0377-2217(90)90375-L – ident: R29 doi: 10.1007/978-1-4615-6357-0 – volume: 152 start-page: 773 year: 2012 ident: R9 publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-011-9921-4 – volume: 254 start-page: 29 year: 2016 ident: R32 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2016.03.042 – ident: R1 doi: 10.1515/9781400830244 – volume: 12 start-page: 237 year: 1991 ident: R35 publication-title: Numer. Funct. Anal. Optim. doi: 10.1080/01630569108816425 – volume: 31 start-page: 133 year: 2005 ident: R18 publication-title: J. Glob. Optim. doi: 10.1007/s10898-003-3780-y – volume: 3 start-page: 2160 year: 2022 ident: R5 publication-title: Math. Oper. Res. doi: 10.1287/moor.2021.1203 – volume: 147 start-page: 106634 year: 2020 ident: R27 publication-title: Comput. Ind. Eng. doi: 10.1016/j.cie.2020.106634 – ident: R12 – volume: 338 start-page: 299 year: 2008 ident: R38 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2007.05.023 – volume: 37 start-page: 303 year: 1998 ident: R26 publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012996311095 – volume: 64 start-page: 289 year: 2015 ident: R10 publication-title: Optimization doi: 10.1080/02331934.2012.745531 – ident: R34 doi: 10.1007/978-94-015-8390-9_3 – volume: 4 start-page: 3201 year: 2019 ident: R4 publication-title: SIAM J. Optim. doi: 10.1137/18M121040X – volume: 34 start-page: 411 year: 2000 ident: R14 publication-title: RAIRO:RO doi: 10.1051/ro:2000122 – volume: 34 start-page: 1799 year: 2024 ident: R6 publication-title: SIAM J. Optim. doi: 10.1137/23M1582382 – ident: R22 – ident: R30 doi: 10.1090/mmono/149 – volume: 103 start-page: 1098 year: 2023 ident: R8 publication-title: Appl. Anal. doi: 10.1080/00036811.2023.2232795 – ident: R24 – volume: 12 start-page: 305 year: 2013 ident: R16 publication-title: Fuzzy Optim. Decis. Mak. doi: 10.1007/s10700-013-9156-y – volume: 15 start-page: 641 year: 1967 ident: R23 publication-title: SIAM J. Appl. Math. doi: 10.1137/0115056 – volume: 10 start-page: 415 year: 2014 ident: R40 publication-title: Pac. J. Optim. – volume: 29 start-page: 743 year: 2019 ident: R3 publication-title: SIAM J. Optim. doi: 10.1137/17M1147330 – volume: 21 start-page: 1523 year: 2011 ident: R21 publication-title: SIAM J. Optim. doi: 10.1137/09075367X – volume: 84 start-page: 155 year: 2022 ident: R7 publication-title: U.P.B. Sci. Bull. Ser. A – volume: 22 start-page: 1245 year: 2018 ident: R19 publication-title: Taiwan. J. Math. Math. Soc. Republic China – volume: 196 start-page: 49 year: 2009 ident: R39 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2008.03.012 – ident: R2 – volume: 5 start-page: 91 year: 2014 ident: R31 publication-title: J. Nonlinear Anal. Optim. – volume: 176 start-page: 46 year: 2007 ident: R37 publication-title: Eur. J. Oper. Res. doi: 10.1016/j.ejor.2005.09.007 – ident: R11 |
| SSID | ssib051866905 ssib051327486 ssj0003353 ssib050921426 |
| Score | 2.334428 |
| Snippet | The growing dependence on optimization models in decision-making has created a demand for tools that can facilitate the formulation and resolution of a broader... |
| SourceID | crossref |
| SourceType | Index Database |
| StartPage | 4259 |
| Title | First and second order necessary optimality conditions for multiobjective programming with interval-valued objective functions on Riemannian manifolds |
| Volume | 58 |
| WOSCitedRecordID | wos001335541500004&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/eLvHCXMwtZ1Lj9MwEMetsnCAA-Ip3rIEtyrZPOzEOVZoq0WCBVUL2ltlO7YaSJOlLcue-Bh8LD4TYzsP7-5lOXBo1LpJG3l-Go_jmb8RepMkkRQyU4EspQ4AijJgvFQBK2OdAV8lsXsDfnmfHx2xk5Pi02Typ6-FOavzpmHn58XpfzU1tIGxTensP5h7-FFogPdgdDiC2eF4LcPPKwjo7JrA1kx2y6lV15w2yhQEmBy5FrzE2oXf5nuXs2XTDW12YSu-OifY526th-e1lU2Q5HVgJMIhUh1PNcNjl1PXTBeVWputkMB1GHUN3daumrgPghfhLHwXLsKPoYlaARp4wV25NXtHpEm-Gdf7V9wOFYdVbYBarXk5EP3d7VgwnX1b1WPzTO-4cKVIq598u_KfbSRkSN4aarqMRgLtNMOVbUtYRALwS6nvwynzWKWeQwb6Cm9wJ4nbbebKwAG-CQxrSovm5kZip5p9UZ_70rg5ZDPadXwaLzftsrv2BrqZ5LQwKYYffh30_g1iMyNwN4R_NE6TnDDvM8uyIhqnb2nqVFT7XujldWm8v2n3u__yAiovMjq-h-52Uxo8cyjeRxPVPEB3PKHLh-i3hRIDlNhBiS2UeIASj1DiEUoMUOKLUGIPSmygxJegxOOpA5S4bfAIJR6gfIQ-zw-O3x4G3Y4ggYRpwi4oRJ5p6CGm8yzSuuSRjKgoGRGEC8mhY6SghSYQmmWCx4qplEVapImEiQXRefoY7TVto54gHOWSxeC-MpVIomLBJRWUSqYzUhQ8Zk_R675bl6dO-GV51dDPrnXWc3R7pPsF2tttfqiX6JY821XbzSvLyF_osKfD |
| 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=First+and+second+order+necessary+optimality+conditions+for+multiobjective+programming+with+interval-valued+objective+functions+on+Riemannian+manifolds&rft.jtitle=R.A.I.R.O.+Recherche+op%C3%A9rationnelle&rft.au=Bhat%2C+Hilal+Ahmad&rft.au=Iqbal%2C+Akhlad&rft.au=Aftab%2C+Mahwash&rft.date=2024-09-01&rft.issn=0399-0559&rft.eissn=2804-7303&rft.volume=58&rft.issue=5&rft.spage=4259&rft.epage=4276&rft_id=info:doi/10.1051%2Fro%2F2024157&rft.externalDBID=n%2Fa&rft.externalDocID=10_1051_ro_2024157 |
| 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 |