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Autori principali: Luxenberg, Eric, Pérez-Piñeiro, David, Diamond, Steven, Boyd, Stephen
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2504.10814
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author Luxenberg, Eric
Pérez-Piñeiro, David
Diamond, Steven
Boyd, Stephen
author_facet Luxenberg, Eric
Pérez-Piñeiro, David
Diamond, Steven
Boyd, Stephen
contents We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows linearly with the number of scenarios, making general-purpose solvers impractical for large-scale problems. Our method combines operator splitting with a specialized $O(m\log m)$ algorithm for projecting onto CVaR constraints, where $m$ is the number of scenarios. The method alternates between solving a linear system and performing parallel projections, onto CVaR constraints using our specialized algorithm and onto box constraints by simple clipping. Numerical examples from several application domains demonstrate that our method outperforms general-purpose solvers by several orders of magnitude on problems with up to millions of scenarios. Our method is implemented in an open-source package called CVQP.
format Preprint
id arxiv_https___arxiv_org_abs_2504_10814
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle An Operator Splitting Method for Large-Scale CVaR-Constrained Quadratic Programs
Luxenberg, Eric
Pérez-Piñeiro, David
Diamond, Steven
Boyd, Stephen
Optimization and Control
We introduce a fast and scalable method for solving quadratic programs with conditional value-at-risk (CVaR) constraints. While these problems can be formulated as standard quadratic programs, the number of variables and constraints grows linearly with the number of scenarios, making general-purpose solvers impractical for large-scale problems. Our method combines operator splitting with a specialized $O(m\log m)$ algorithm for projecting onto CVaR constraints, where $m$ is the number of scenarios. The method alternates between solving a linear system and performing parallel projections, onto CVaR constraints using our specialized algorithm and onto box constraints by simple clipping. Numerical examples from several application domains demonstrate that our method outperforms general-purpose solvers by several orders of magnitude on problems with up to millions of scenarios. Our method is implemented in an open-source package called CVQP.
title An Operator Splitting Method for Large-Scale CVaR-Constrained Quadratic Programs
topic Optimization and Control
url https://arxiv.org/abs/2504.10814