An alternative approach to well-posedness of McKean-Vlasov equations arising in Consensus-Based Optimization

Mathematics > Optimization and Control [Submitted on 22 Dec 2025 (v1), last revised 18 Jun 2026 (this version, v4)] Title:An alternative approach to well-posedness of McKean-Vlasov equations arising in Consensus-Based Optimization View PDF HTML (experimental)Abstract:In this work we study the mean-field description of Consensus-Based Optimization (CBO), a derivative-free particle optimization method. Such a description is provided by a non-local SDE of McKean-Vlasov type, whose fields lack of global Lipschitz continuity. We propose a novel approach to prove the well-posedness of the mean-field CBO equation based on a truncation argument. The latter is performed through the introduction of a cut-off function, defined on the space of probability measures, acting on the fields. This procedure allows us to study the well-posedness problem in the classical framework of Sznitman. Through this argument, we recover the established result on the existence of strong solutions, and we extend the class of solutions for which pathwise uniqueness holds. Submission history From: Alessandro Baldi [view email][v1] Mon, 22 Dec 2025 14:45:29 UTC (20 KB) [v2] Tue, 23 Dec 2025 21:37:47 UTC (20 KB) [v3] Sat, 27 Dec 2025 02:09:35 UTC (21 KB) [v4] Thu, 18 Jun 2026 16:30:10 UTC (22 KB) Current browse context: math.OC References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.