Improved Conjugate Gradient Methods Based on Scaling Techniques for Large-Scale Unconstrained Optimization

Improved Conjugate Gradient Methods Based on Scaling Techniques for Large-Scale Unconstrained Optimization | 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 Improved Conjugate Gradient Methods Based on Scaling Techniques for Large-Scale Unconstrained Optimization Mehiddin Al-Baali, Amal AlSaidi, Giovanni Fasano, Massimo Roma This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7529509/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract The well-known class of Conjugate Gradient (CG) methods represents an important computational tool in solving large-scale unconstrained optimization problems. We study the recent class of scaled CG techniques and propose some choices for the parameter, which guarantee the sufficient descent condition. The quasi-Newton feature is also introduced to the class of methods in a sense to be defined. Hence, we enforce the global convergence property for several choices of the parameter in several cases. The behavior of the proposed methods is tested by applying them to a set of standard test problems. The reported numerical results show that the proposed scaled techniques improve the performance of several CG methods substantially. Unconstrained optimization large-scale nonlinear conjugate gradient methods quasi-Newton condition Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 14 Oct, 2025 Reviewers invited by journal 14 Oct, 2025 Editor assigned by journal 15 Sep, 2025 Submission checks completed at journal 14 Sep, 2025 First submitted to journal 03 Sep, 2025 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-7529509","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":529431493,"identity":"ac30a561-c394-4f82-8f07-6ac64a20328d","order_by":0,"name":"Mehiddin 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