AS-BOX: Additional Sampling Method for  Weighted Sum Problems with Box Constraints

AS-BOX: Additional Sampling Method for Weighted Sum Problems with Box Constraints | 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 AS-BOX: Additional Sampling Method for Weighted Sum Problems with Box Constraints Nataša Krejić, Nataša Krklec Jerinkić, Tijana Ostojić, Nemanja Vučićević This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7486649/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Dec, 2025 Read the published version in Numerical Algorithms → Version 1 posted 9 You are reading this latest preprint version Abstract A class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. We propose a novel stochastic optimization method, named AS-BOX (\text{A}ddi\-ti\-onal \text{S}ampling for \text{BOX} constraints), that combines projected gradient directions with adaptive variable sample size strategies and nonmonotone line search. The method dynamically adjusts the batch size based on progress with respect to the additional sampling function and on structural consistency of the projected direction, enabling practical adaptivity of AS-BOX, while ensuring theoretical support. We establish almost sure convergence under standard assumptions and provide complexity bounds. Numerical experiments demonstrate the efficiency and competitiveness of the proposed method compared to state-of-the-art algorithms. MSC Classification: 90C15,90C26, 90C30, 65K05 Projected Gradient Methods Sample Average Approximation Adaptive Variable Sample Size Strategies Non-monotone Line Search Additional Sampling Almost Sure Convergence Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 01 Dec, 2025 Read the published version in Numerical Algorithms → Version 1 posted Editorial decision: Revision requested 16 Oct, 2025 Reviews received at journal 16 Oct, 2025 Reviews received at journal 07 Oct, 2025 Reviewers agreed at journal 08 Sep, 2025 Reviewers agreed at journal 07 Sep, 2025 Reviewers invited by journal 07 Sep, 2025 Editor assigned by journal 02 Sep, 2025 Submission checks completed at journal 01 Sep, 2025 First submitted to journal 29 Aug, 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-7486649","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":511780006,"identity":"9ff8a393-fe06-4e49-b2ea-c57f4e13da21","order_by":0,"name":"Nataša Krejić","email":"","orcid":"","institution":"University of Novi Sad","correspondingAuthor":false,"prefix":"","firstName":"Nataša","middleName":"","lastName":"Krejić","suffix":""},{"id":511780007,"identity":"b5d8dcce-cb13-4f6b-8262-faea6f2d0652","order_by":1,"name":"Nataša Krklec Jerinkić","email":"","orcid":"","institution":"University of Novi Sad","correspondingAuthor":false,"prefix":"","firstName":"Nataša","middleName":"Krklec","lastName":"Jerinkić","suffix":""},{"id":511780008,"identity":"a102ef71-46b6-434f-b98c-aba1b6a6c54e","order_by":2,"name":"Tijana Ostojić","email":"","orcid":"","institution":"University of Novi Sad","correspondingAuthor":false,"prefix":"","firstName":"Tijana","middleName":"","lastName":"Ostojić","suffix":""},{"id":511780009,"identity":"b3ff5ab3-7508-446f-b695-2fbf03a98e76","order_by":3,"name":"Nemanja Vučićević","email":"data:image/png;base64,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","orcid":"","institution":"University of Kragujevac","correspondingAuthor":true,"prefix":"","firstName":"Nemanja","middleName":"","lastName":"Vučićević","suffix":""}],"badges":[],"createdAt":"2025-08-29 08:38:37","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7486649/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7486649/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11075-025-02275-7","type":"published","date":"2025-12-01T15:57:43+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":97723878,"identity":"ef5e22f1-c6a6-4806-a9ff-60db6a152fc3","added_by":"auto","created_at":"2025-12-08 16:09:00","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":542941,"visible":true,"origin":"","legend":"","description":"","filename":"ASBOX.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7486649/v1_covered_61ff2011-a3a7-4289-be8b-0c7e28797513.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"AS-BOX: Additional Sampling Method for Weighted Sum Problems with Box Constraints","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"numerical-algorithms","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"numa","sideBox":"Learn more about [Numerical Algorithms](http://link.springer.com/journal/11075)","snPcode":"11075","submissionUrl":"https://submission.nature.com/new-submission/11075/3","title":"Numerical Algorithms","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Projected Gradient Methods, Sample Average Approximation, Adaptive Variable Sample Size Strategies, Non-monotone Line Search, Additional Sampling, Almost Sure Convergence","lastPublishedDoi":"10.21203/rs.3.rs-7486649/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7486649/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. 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