A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning

A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning | 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 A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning Xianzhen Jiang, Guoqing Sun, Jinbao Jian This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4407844/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Conjugate gradient method is one of the most effective schemes to deal with large-scale optimization problems. In this study, three classes of parameters for the Dai-Liao conjugate condition are provided to be chosen, and thus a new Dai-Liao conjugate parameter is derived. Making a truncation for the conjugate parameter and introducing a restart procedure into the search direction, a family of improved Dai-Liao conjugate gradient methods is proposed. It is sufficient descent at each iteration without depending on the choice of the line search criterion. Under usual assumptions, and using the weak Wolfe line search criterion to yield its steplength, its strong convergence is proved. Finally, choosing a specific algorithm from this family to solve large-scale unconstrained optimization problems, image restorations and machine learning, the corresponding numerical results show that the new algorithm is promising. Mathematics Subject Classification (2020) 65K05 · 90C52 · 90C53 · 90C56 Unconstrained optimization Dai-Liao conjugate gradient method Weak Wolfe line search Strong convergence Image restoration Machine learning Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version 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-4407844","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":307594859,"identity":"dfd24564-4087-4860-90be-5993d5aefb71","order_by":0,"name":"Xianzhen Jiang","email":"","orcid":"","institution":"Guangxi Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Xianzhen","middleName":"","lastName":"Jiang","suffix":""},{"id":307594860,"identity":"cd9c02a2-e243-4344-b5bc-1b719c0f3bda","order_by":1,"name":"Guoqing Sun","email":"","orcid":"","institution":"Guangxi Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Guoqing","middleName":"","lastName":"Sun","suffix":""},{"id":307594861,"identity":"62182d86-94a1-44cb-a3d1-488da5108b2c","order_by":2,"name":"Jinbao Jian","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAyklEQVRIiWNgGAWjYBACxmYgIdlgA+HxkKAljQQtEH0Nh0nQwtzO/OyB5Y7zdhtuJDA+eNvGIG9O2GFs5gaSZ24nz5yRwGw4t43BcGcDQS0MZhKSbbeT+SUS2KR52xgSDA4Q1ML+DajlXDKbRAL7byK18IBsOWAHsoWZWC1lEpJnkhMkex42S845J2G4gZAWw/7j26Qld9jZGxxPPvjhTZmNPEFbDBuAAS3BwJDYAIwdIF+CgHogkAc57gMDgz1hpaNgFIyCUTBiAQBvrDqAORO0RAAAAABJRU5ErkJggg==","orcid":"","institution":"Guangxi Minzu University","correspondingAuthor":true,"prefix":"","firstName":"Jinbao","middleName":"","lastName":"Jian","suffix":""}],"badges":[],"createdAt":"2024-05-12 08:53:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4407844/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4407844/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":65997383,"identity":"1fb3999e-f5ef-4765-9c27-f1a2e2c02644","added_by":"auto","created_at":"2024-10-06 03:16:44","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3310824,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4407844/v1_covered_a8e39cec-5a59-4071-acb6-cf59632d65a7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"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":"Unconstrained optimization, Dai-Liao conjugate gradient method, Weak Wolfe line search, Strong convergence, Image restoration, Machine learning","lastPublishedDoi":"10.21203/rs.3.rs-4407844/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4407844/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eConjugate gradient method is one of the most effective schemes to deal with large-scale optimization problems. In this study, three classes of parameters for the Dai-Liao conjugate condition are provided to be chosen, and thus a new Dai-Liao conjugate parameter is derived. Making a truncation for the \u0026nbsp;conjugate parameter and introducing a restart procedure into the search direction, a family of improved Dai-Liao conjugate gradient methods is proposed. It is sufficient descent at each iteration without depending on the choice of the line search criterion. Under usual assumptions, and using the weak Wolfe line search criterion to yield its steplength, its strong convergence is proved. Finally, choosing a specific algorithm from this family to solve large-scale unconstrained optimization problems, \u0026nbsp;image restorations and machine learning, the corresponding numerical results show that the new algorithm is promising.\u003c/p\u003e\n\u003cp\u003eMathematics Subject Classification (2020) 65K05 · 90C52 · 90C53 · 90C56\u003c/p\u003e","manuscriptTitle":"A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-05-30 10:46:22","doi":"10.21203/rs.3.rs-4407844/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":"31488383-9af5-4e4f-9f67-c882226315d4","owner":[],"postedDate":"May 30th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-10-06T03:08:25+00:00","versionOfRecord":[],"versionCreatedAt":"2024-05-30 10:46:22","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4407844","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4407844","identity":"rs-4407844","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}