A Novel approach for the solvability of Monotone Bilevel framework for split variational inequality problems within Hilbert setting optimization

A Novel approach for the solvability of Monotone Bilevel framework for split variational inequality problems within Hilbert setting 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 A Novel approach for the solvability of Monotone Bilevel framework for split variational inequality problems within Hilbert setting optimization Mohammed Rabie, Musa A. Olona, Zakaria I. Ali This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9263330/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 presents a novel algorithm modified inertial Tseng extragradient approach with a self-adaptive step size for the approximation of the solutions for the celebrated bilevel split variational inequality problem in the framework of Hilbert setting. Using the approach of projections onto a constructible half-space, we establish the required strong convergence result for the proposed iterative technique. Our method does not require prior techniques of the Lipschitz type constant for the cost operators. Finally, we present several numerical experi- ments that show how much efficient and applicable the proposed techniques are in contrast with the well-known existing results. MSC Classification: 47H06 , 47H09 , 47J05 , 47J25 Applied Mathematics Bilevel variational inequality problem Split bilvel variational inequality problem iterative techniques Full Text Additional Declarations The authors declare no competing interests. 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-9263330","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":614341001,"identity":"28862818-8e78-47fb-997c-86665a18fbe0","order_by":0,"name":"Mohammed Rabie","email":"","orcid":"","institution":"Shaqra Universit","correspondingAuthor":false,"prefix":"","firstName":"Mohammed","middleName":"","lastName":"Rabie","suffix":""},{"id":614341002,"identity":"2ff26f1e-4858-468c-a3f8-93ee9300d454","order_by":1,"name":"Musa A. 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