Robust Hybrid Conjugate Gradient Algorithms via Projection for Large-Scale Optimization and Compressed Sensing

Robust Hybrid Conjugate Gradient Algorithms via Projection for Large-Scale Optimization and Compressed Sensing | 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 Robust Hybrid Conjugate Gradient Algorithms via Projection for Large-Scale Optimization and Compressed Sensing Maryam Khoshsimaye-Bargard, Farshid Abdollahi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7287801/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 This paper introduces two novel and highly effective hybrid conjugate gradient (CG) methods, integrating the theoretical strengths of the Dai--Yuan (DY) method with the computational efficiency of the Rivaie--Mustafa--Ismail--Leong (RMIL) method. These approaches derive from a convex combination of their conjugate parameters, differentiated by how the hybridization parameter is calculated: one ensures conjugacy independent of any line search, while the other draws inspiration from quasi--Newton (QN) methods and the standard secant condition. These methods are particularly well-suited for addressing complex, large-scale unconstrained optimization problems prevalent in various scientific and engineering disciplines. Both methods guarantee the sufficient descent property by projecting the search direction onto the gradient's orthogonal subspace, independent of line search or objective function convexity. We rigorously establish the global convergence analysis for general objective functions under standard assumptions. Comprehensive numerical experiments on CUTEr test problems and a compressed sensing application demonstrate the superior performance, remarkable robustness, and enhanced computational efficiency of our proposed algorithms compared to existing state-of-the-art CG methods, thereby offering significant advancements in optimization techniques. MSC Classification: 90C06; 49M37 Unconstrained optimization Hybrid conjugate gradient method Projecting strategy Suffcient descent property Global convergence Compressed sensing 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. 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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-7287801","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":502275426,"identity":"b61ae8fc-da50-4425-a1e3-88dc3b8a9742","order_by":0,"name":"Maryam Khoshsimaye-Bargard","email":"data:image/png;base64,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","orcid":"","institution":"Shiraz University","correspondingAuthor":true,"prefix":"","firstName":"Maryam","middleName":"","lastName":"Khoshsimaye-Bargard","suffix":""},{"id":502275428,"identity":"946147aa-32d0-4a46-941b-db988867715c","order_by":1,"name":"Farshid Abdollahi","email":"","orcid":"","institution":"Shiraz University","correspondingAuthor":false,"prefix":"","firstName":"Farshid","middleName":"","lastName":"Abdollahi","suffix":""}],"badges":[],"createdAt":"2025-08-04 06:53:50","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7287801/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7287801/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":99312290,"identity":"e32aa714-1b12-49b9-9ec9-bad42d82997c","added_by":"auto","created_at":"2025-12-31 16:18:40","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1190705,"visible":true,"origin":"","legend":"","description":"","filename":"KhoshsimayeAbdollahiNAV1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7287801/v1_covered_16e550dd-064a-4e65-aa12-7462cb07849b.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Robust Hybrid Conjugate Gradient Algorithms via Projection for Large-Scale Optimization and Compressed Sensing","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, Hybrid conjugate gradient method, Projecting strategy, Suffcient descent property, Global convergence, Compressed sensing","lastPublishedDoi":"10.21203/rs.3.rs-7287801/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7287801/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces two novel and highly effective hybrid conjugate gradient (CG) methods, integrating the theoretical strengths of the Dai--Yuan (DY) method with the computational efficiency of the Rivaie--Mustafa--Ismail--Leong (RMIL) method. 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