Projected quasisubgradient method for Hölder continuous quasi-convex multiobjective optimization

Projected quasisubgradient method for Hölder continuous quasi-convex multiobjective 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 Projected quasisubgradient method for Hölder continuous quasi-convex multiobjective optimization FEEROZ BABU, Debdas Ghosh, Muzaffar Sarkar Raju This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9306185/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract We propose a projected quasisubgradient method for constrained, nondifferentiable, quasi-convex multiobjective minimization problems. Unlike existing approaches that rely on Lipschitz continuity, our method only requires H\"older continuity of the objective components, thereby covering a broader class of quasi-convex functions. Under these assumptions, we establish convergence of the generated sequence to a Pareto optimal solution and derive a sublinear rate of convergence that explicitly depends on the H\"older parameters, recovering the Lipschitz case as a special instance. The method is simple to implement, robust to nondifferentiability, and theoretically well-defined. Numerical experiments including application on portfolio optimization, electric vehicle charging network optimization and smart grid energy management are provided. Dolan-Moré performance profiles indicate that the proposed method outperforms. Mathematics Subject Classification (2000) 49M37; 49J52; 90C29; 90C30 Multiobjective optimization Pareto optimality quasiconvex functions nonsmooth optimization projected quasi-subgradient method H¨older continuity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 08 May, 2026 Reviews received at journal 30 Apr, 2026 Reviewers agreed at journal 30 Apr, 2026 Reviewers agreed at journal 20 Apr, 2026 Reviewers agreed at journal 09 Apr, 2026 Reviewers invited by journal 07 Apr, 2026 Editor assigned by journal 06 Apr, 2026 Submission checks completed at journal 04 Apr, 2026 First submitted to journal 02 Apr, 2026 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. 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