Optimality-Induced Stabilization in Constrained Networked Optimization

Optimality-Induced Stabilization in Constrained Networked 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Article Optimality-Induced Stabilization in Constrained Networked Optimization Nam Anh Quach This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8987359/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 Stability of networked stochastic systems is traditionally achieved through explicitly engineered control policies that enforce negative Lyapunov drift. In contrast, many operational infrastructures are governed by economic optimization objectives rather than stabilizing design constraints. This paper identifies a structural mechanism under which stability emerges as a necessary consequence of optimality in constrained dynamic optimization. We consider controlled Markov systems with convex capacity regions induced by shared resource constraints and stage costs composed of a convex, coercive congestion potential and a control cost. We prove that if the exogenous load vector lies strictly in the interior of the capacity region, then every optimal stationary policy for the discounted problem satisfies a Foster–Lyapunov drift inequality outside a compact set. Consequently, the induced state process is positive recurrent. Stability is not imposed—it is structurally enforced by convex capacity geometry and coercive cost growth. Complementing this interior result, we establish a sharp capacity boundary theorem: if the load lies outside the convex capacity region, no admissible policy can render the system positive recurrent. The convex throughput polytope therefore characterizes the stabilizable load set exactly. A multi-terminal transportation network with shared polyhedral constraints illustrates the geometric phase transition predicted by the theory. The results reveal an intrinsic alignment between economic optimality and stochastic stabilization in convex networked systems. Operations Research Applied Mathematics Convex capacity region Foster–Lyapunov stability Markov decision processes Coercive congestion costs Networked stochastic optimization Positive recurrence Capacity boundary Dynamic resource allocation 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-8987359","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":598107779,"identity":"b001b306-8364-47b2-8f8e-d52d51c07c48","order_by":0,"name":"Nam Anh Quach","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYLACxgYQycP4+E8FkGZmbiBaC7MBzxmQFkbitbBJ8LYhuDiBOfvpxM+FO6wT+9vPHpCQnFcbzd8O1PKjYhtOLZY9uZulZ55JT5xxJi/BwHDb8dwZhxkbGHvO3MapxeBA7gZp3rbDiQ03eAwSErcdy20AamFmbMOj5fzbzb9BWuYDtRw4OOdY7nyCWm7kbgPbsuEGj2FjY0NN7gbCWt5us+ZtSzfeeCbHmJnh2IHcjUAtB/H65Xzu5tu8bday846fMf/NUFOXO+/84YMPflTg1gIFzDDGYTB5gJB6ZC11RCgeBaNgFIyCkQYAJ8Fh8iX1/zgAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0000-7962-6695","institution":"Hong Bang International University","correspondingAuthor":true,"prefix":"","firstName":"Nam","middleName":"Anh","lastName":"Quach","suffix":""}],"badges":[],"createdAt":"2026-02-27 11:21:47","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-8987359/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8987359/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103730033,"identity":"5aa5cccf-762a-4098-9bed-43cade2c7902","added_by":"auto","created_at":"2026-03-02 09:03:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":866654,"visible":true,"origin":"","legend":"","description":"","filename":"OptimalityInducedStabilizationinNetworkedOptimization.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8987359/v1_covered_1ec2ba27-ade7-4b3a-9f0a-23115735126e.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eOptimality-Induced Stabilization in Constrained Networked Optimization\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Hong Bang International University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Convex capacity region, Foster–Lyapunov stability, Markov decision processes, Coercive congestion costs, Networked stochastic optimization, Positive recurrence, Capacity boundary, Dynamic resource allocation","lastPublishedDoi":"10.21203/rs.3.rs-8987359/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8987359/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eStability of networked stochastic systems is traditionally achieved through explicitly engineered control policies that enforce negative Lyapunov drift. In contrast, many operational infrastructures are governed by economic optimization objectives rather than stabilizing design constraints. This paper identifies a structural mechanism under which stability emerges as a necessary consequence of optimality in constrained dynamic optimization. We consider controlled Markov systems with convex capacity regions induced by shared resource constraints and stage costs composed of a convex, coercive congestion potential and a control cost. We prove that if the exogenous load vector lies strictly in the interior of the capacity region, then every optimal stationary policy for the discounted problem satisfies a Foster\u0026ndash;Lyapunov drift inequality outside a compact set. Consequently, the induced state process is positive recurrent. Stability is not imposed\u0026mdash;it is structurally enforced by convex capacity geometry and coercive cost growth. Complementing this interior result, we establish a sharp capacity boundary theorem: if the load lies outside the convex capacity region, no admissible policy can render the system positive recurrent. The convex throughput polytope therefore characterizes the stabilizable load set exactly. A multi-terminal transportation network with shared polyhedral constraints illustrates the geometric phase transition predicted by the theory. 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