Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures

[2607.17018] Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2607.17018 (math) [Submitted on 19 Jul 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures Authors: Shibshankar Dey , Sanjay Mehrotra View PDF HTML (experimental) Abstract: We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of the nominal mixture-support parameters. To address this limitation, we describe the ambiguity set of distributions by developing a novel formulation of a Wasserstein-2 metric that uses the Bures-Wasserstein (BW) metric over probability measures with finite second moments. Unlike FDR, which generally sets finitely many empirical support points a priori, the proposed ambiguity set allows the worst-case distribution to endogenously determine both how many mixture components receive mass and where their means and covariances lie within a continuous support. For the resulting ambiguity set, under mild regularity conditions, we prove strong duality for the inner worst-case chance-constraint problem and derive its semi-infinite reformulation. We then develop an adaptive cutting-surface algorithm, which endogenously determines the locations of mixture components receiving mass, and the mean and covariances of the Gaussian distributions at these locations. The algorithm attains any prescribed optimality gap in finitely many iterations, while a block-alternating local search identifies new components. A case study using the electric-vehicle charging-station energy-allocation problem demonstrates the framework's practical value in achieving any reliability targets. CDR also induces structural changes in energy allocations, unlike FDR, whose allocations remain close to the nominal solution. Subjects: Optimization and Control (math.OC) ; Machine Learning (cs.LG) Cite as: arXiv:2607.17018 [math.OC] (or arXiv:2607.17018v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2607.17018 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shibshankar Dey [ view email ] [v1] Sun, 19 Jul 2026 01:10:05 UTC (5,872 KB) [v2] Thu, 27 Aug 2026 21:04:25 UTC (5,393 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2026-07 Change to browse by: cs cs.LG 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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