Optimality results for nondifferentiable multiobjective fractional programming problems under E-B-invexity | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Optimality results for nondifferentiable multiobjective fractional programming problems under E-B-invexity S. K. Mishra, Dhruv Singh, Pankaj Kumar, Vandana Singh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4250147/v2 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Oct, 2024 Read the published version in Results in Control and Optimization → Version 2 posted You are reading this latest preprint version Show more versions Abstract In this study, we address nonconvex multiobjective fractional pro- gramming problems involving E-differentiable functions (MF PE). The so-called E-Karush–Kuhn–Tucker suffcient E-optimality conditions are established for nonsmooth vector optimization problems under the E-B-invexity hypothesis. To illustrate the established results, we present an example in which the functions involved are E-B-invex. MSC Classification: 90C32 , 90C46 , 49J52 , 90C30 , 90C29 E-differentiable multiobjective fractional optimization problems E-B-invex functions E-optimality conditions Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Published Journal Publication published 14 Oct, 2024 Read the published version in Results in Control and Optimization → Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4250147","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":305765813,"identity":"0af5504a-5695-45e5-9041-83fd7a77b984","order_by":0,"name":"S. K. Mishra","email":"","orcid":"","institution":"Banaras Hindu University","correspondingAuthor":false,"prefix":"","firstName":"S.","middleName":"K.","lastName":"Mishra","suffix":""},{"id":305765814,"identity":"57bfc0a0-53d1-46b8-ba6a-16aecb42587f","order_by":1,"name":"Dhruv Singh","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABBklEQVRIiWNgGAWjYDCCG2BSAoiYj39IqLBJMGCAiRDWwpbG8OFMGtFaQGp4zBhnth2GacEN+G73PpPm+WORJx/dYPaYt+18nrlEAuOHHwwWebi0SN45bibN2yZRbHjnQLoxz7nbxZYzEpglexgkinFpMbiRxiY5s0EiceOMhAPSPGW3EzfcSGCQBrozsQGflhl/QFoSG6R52M6BtDD/JqRF4gObROJ8iWSg3rYDIC1seG2RvJHGbPGxTSJxg0Qas8GHM8nFBmcetln2GODWwncjjfFGwp+6xPkz8j8+SKiwyzM4nnz4xo+KOpxaEC48AGcyAhUTjB0gkCdo6CgYBaNgFIxYAABhX128NnXSqgAAAABJRU5ErkJggg==","orcid":"","institution":"Banaras Hindu University","correspondingAuthor":true,"prefix":"","firstName":"Dhruv","middleName":"","lastName":"Singh","suffix":""},{"id":305765815,"identity":"26d67b3d-d4b6-4c66-9a7b-9d41c661b7df","order_by":2,"name":"Pankaj Kumar","email":"","orcid":"","institution":"Banaras Hindu University","correspondingAuthor":false,"prefix":"","firstName":"Pankaj","middleName":"","lastName":"Kumar","suffix":""},{"id":305765816,"identity":"ada9f944-3706-4985-ae37-760d5fe01d0f","order_by":3,"name":"Vandana Singh","email":"","orcid":"","institution":"Banaras Hindu University","correspondingAuthor":false,"prefix":"","firstName":"Vandana","middleName":"","lastName":"Singh","suffix":""}],"badges":[],"createdAt":"2024-04-11 04:14:19","currentVersionCode":2,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-4250147/v2","doiUrl":"https://doi.org/10.21203/rs.3.rs-4250147/v2","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1016/j.rico.2024.100486","type":"published","date":"2024-10-15T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":66798348,"identity":"f1b0f53b-d1fc-4bd2-bb53-1818ad24ab51","added_by":"auto","created_at":"2024-10-16 14:35:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":280271,"visible":true,"origin":"","legend":"","description":"","filename":"EBinvexity.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4250147/v2_covered_9561afe1-1406-4798-9a42-db194bb905fb.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimality results for nondifferentiable multiobjective fractional programming problems under E-B-invexity\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"
[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"E-differentiable, multiobjective fractional optimization problems, E-B-invex functions, E-optimality conditions","lastPublishedDoi":"10.21203/rs.3.rs-4250147/v2","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4250147/v2","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, we address nonconvex multiobjective fractional pro-\u003c/p\u003e\n\u003cp\u003egramming problems involving E-differentiable functions (MF PE).\u003c/p\u003e\n\u003cp\u003eThe so-called E-Karush–Kuhn–Tucker suffcient E-optimality conditions\u003c/p\u003e\n\u003cp\u003eare established for nonsmooth vector optimization problems under\u003c/p\u003e\n\u003cp\u003ethe E-B-invexity hypothesis. To illustrate the established results, we\u003c/p\u003e\n\u003cp\u003epresent an example in which the functions involved are E-B-invex.\u003c/p\u003e\n\u003cp\u003eMSC Classification: 90C32 , 90C46 , 49J52 , 90C30 , 90C29\u003c/p\u003e","manuscriptTitle":"Optimality results for nondifferentiable multiobjective fractional programming problems under E-B-invexity","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2024-10-07 13:41:11","doi":"10.21203/rs.3.rs-4250147/v2","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"
[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}},{"code":1,"date":"2024-05-23 05:51:21","doi":"10.21203/rs.3.rs-4250147/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"
[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7b39e5ca-99d6-4a09-8083-185165a146b2","owner":[],"postedDate":"October 7th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-10-16T14:35:53+00:00","versionOfRecord":{"articleIdentity":"rs-4250147","link":"https://doi.org/10.1016/j.rico.2024.100486","journal":{"identity":"results-in-control-and-optimization","isVorOnly":true,"title":"Results in Control and Optimization"},"publishedOn":"2024-10-15 00:00:00","publishedOnDateReadable":"October 15th, 2024"},"versionCreatedAt":"2024-10-07 13:41:11","video":"","vorDoi":"10.1016/j.rico.2024.100486","vorDoiUrl":"https://doi.org/10.1016/j.rico.2024.100486","workflowStages":[]},"version":"v2","identity":"rs-4250147","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4250147","identity":"rs-4250147","version":["v2"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}
Text is read by the "Ask this paper" AI Q&A widget below.
Extraction quality varies by source — PMC NXML preserves structure
cleanly, OA-HTML may include some navigation residue, and OA-PDF can
have broken hyphenation. The publisher copy
(via DOI)
is the canonical version.