Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search

Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search | 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 Nonlinear Derivative-free Constrained Optimization with a Penalty-Interior Point Method and Direct Search Andrea Brilli, Ana L. Custódio, Giampaolo Liuzzi, Everton J. Silva This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6730565/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Apr, 2026 Read the published version in Numerical Algorithms → Version 1 posted 9 You are reading this latest preprint version Abstract In this work, we propose the joint use of a mixed penalty-interior point method and direct search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear inequality constraints is divided into two groups: one treated with a logarithmic barrier approach, and another, along with the equality constraints, addressed using a penalization term. This strategy, is adapted and incorporated into a direct search method, enabling the effective handling of general nonlinear constraints. Convergence to KKT-stationary points is established under continuous differentiability assumptions, without requiring any kind of convexity. Using CUTEst test problems, numerical experiments demonstrate the robustness, efficiency, and overall effectiveness of the proposed method, when compared with state-of-the-art solvers. Derivative-free optimization Constrained optimization Interior point methods Direct search Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 01 Apr, 2026 Read the published version in Numerical Algorithms → Version 1 posted Editorial decision: Revision requested 19 Jul, 2025 Reviews received at journal 18 Jul, 2025 Reviews received at journal 02 Jul, 2025 Reviewers agreed at journal 04 Jun, 2025 Reviewers agreed at journal 02 Jun, 2025 Reviewers invited by journal 02 Jun, 2025 Editor assigned by journal 02 Jun, 2025 Submission checks completed at journal 02 Jun, 2025 First submitted to journal 23 May, 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. 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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-6730565","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":465348034,"identity":"1a839987-0e14-47dc-80f1-65f8fcdc9d1e","order_by":0,"name":"Andrea Brilli","email":"","orcid":"","institution":"Sapienza University of Rome","correspondingAuthor":false,"prefix":"","firstName":"Andrea","middleName":"","lastName":"Brilli","suffix":""},{"id":465348035,"identity":"a4c2db83-0aed-4caa-b675-351f308687c2","order_by":1,"name":"Ana L. 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