A Subgradient Projection Method for Quasiconvex Minimization

A Subgradient Projection Method for Quasiconvex Minimization | 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 Subgradient Projection Method for Quasiconvex Minimization Felipe Lara, Raúl Marcavillaca, Juan Choque This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4022333/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Sep, 2024 Read the published version in Positivity → Version 1 posted 8 You are reading this latest preprint version Abstract In this paper, a subgradient projection method for quasiconvex minimization problems is provided. By using strong subdifferentials, it is proved that the generated sequence of the proposed algorithm converges to the solution of the minimization problem of a proper, lower semicontinuous and strongly quasiconvex function (in the sense of Polyak [18]) under the same assumptions than for convex functions with the convex subdifferential. Furthermore, a quasi-linear convergence rate of the iterates, which extends similar results for the general quasiconvex case, is also provided. Subgradient methods First-order methods Nonconvex optimization Generalized convexity Quasiconvexity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Sep, 2024 Read the published version in Positivity → Version 1 posted Editorial decision: Revision requested 20 Aug, 2024 Reviewers agreed at journal 18 Jul, 2024 Reviews received at journal 17 Jul, 2024 Reviewers agreed at journal 11 Mar, 2024 Reviewers invited by journal 11 Mar, 2024 Editor assigned by journal 09 Mar, 2024 Submission checks completed at journal 08 Mar, 2024 First submitted to journal 06 Mar, 2024 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. 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