An Exact Algorithm for Mixed-Integer Bilevel Stochastic Problem

[2606.29344] An Exact Algorithm for Mixed-Integer Bilevel Stochastic Problem Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2606.29344 (math) [Submitted on 28 Jun 2026 ( v1 ), last revised 25 Aug 2026 (this version, v3)] Title: An Exact Algorithm for Mixed-Integer Bilevel Stochastic Problem Authors: Tomás Lagos , Dmytro Matsypura View PDF HTML (experimental) Abstract: We study a class of mixed-integer bilevel stochastic programs in which the leader commits to a first-stage decision before uncertainty is realized, and the follower solves a mixed-integer optimization problem for each revealed scenario. Due to the hierarchical structure and discrete variables at both levels, these problems are inherently $\Sigma_2^p$-hard, rendering standard single-level reformulations computationally intractable. To address this challenge, we develop an exact algorithm that combines deterministic value-function reformulations with scenario-wise decomposition. Specifically, we propose an extended single-level reformulation and a corresponding relaxation that enable scenario decomposition. We then introduce a stochastic subgradient cutting-plane scheme that dynamically generates follower optimality cuts and updates the Lagrange multipliers. We prove that, under boundedness assumptions, our algorithm converges in finite time to a global optimum and provides valid upper and lower bounds throughout its execution. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2606.29344 [math.OC] (or arXiv:2606.29344v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2606.29344 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Dmytro Matsypura [ view email ] [v1] Sun, 28 Jun 2026 11:21:13 UTC (196 KB) [v2] Wed, 1 Jul 2026 01:40:47 UTC (196 KB) [v3] Tue, 25 Aug 2026 03:26:16 UTC (76 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-06 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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 . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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