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Relaxations for probabilistically constrained stochastic programming problems: review and extensions.

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Title: Relaxations for probabilistically constrained stochastic programming problems: review and extensions.
Authors: Lejeune, Miguel A.1 (AUTHOR) mlejeune@gwu.edu, Prékopa, A.2 (AUTHOR)
Source: Annals of Operations Research. Nov2025, Vol. 354 Issue 3, p1227-1248. 22p.
Subjects: Stochastic programming, Random variables, Numerical integration, Convex domains
Abstract: We consider probabilistically constrained stochastic programming problems, in which the random variables are in the right-hand sides of the stochastic inequalities defining the joint chance constraints. Problems of that kind arise in a variety of contexts, and are particularly difficult to solve for random variables with continuous joint distributions, because the calculation of the cumulative distribution function and its gradient values involves numerical integration and/or simulation in large dimensional spaces. We revisit known and provide new relaxations extensions to various probability bounding schemes that permit to approximate the feasible set of joint probabilistic constraints. The derived mathematical formulations relax the requirement to handle large multivariate cumulative distribution functions and involve instead the computation of marginal and bivariate cumulative distribution functions. We analyze the convexity of and computational challenges posed by the inferred relaxations [ABSTRACT FROM AUTHOR]
Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Relaxations for probabilistically constrained stochastic programming problems: review and extensions.
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  Data: <searchLink fieldCode="JN" term="%22Annals+of+Operations+Research%22">Annals of Operations Research</searchLink>. Nov2025, Vol. 354 Issue 3, p1227-1248. 22p.
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  Data: We consider probabilistically constrained stochastic programming problems, in which the random variables are in the right-hand sides of the stochastic inequalities defining the joint chance constraints. Problems of that kind arise in a variety of contexts, and are particularly difficult to solve for random variables with continuous joint distributions, because the calculation of the cumulative distribution function and its gradient values involves numerical integration and/or simulation in large dimensional spaces. We revisit known and provide new relaxations extensions to various probability bounding schemes that permit to approximate the feasible set of joint probabilistic constraints. The derived mathematical formulations relax the requirement to handle large multivariate cumulative distribution functions and involve instead the computation of marginal and bivariate cumulative distribution functions. We analyze the convexity of and computational challenges posed by the inferred relaxations [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Annals of Operations Research is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10479-018-2934-8
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      – SubjectFull: Stochastic programming
        Type: general
      – SubjectFull: Random variables
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      – SubjectFull: Numerical integration
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      – SubjectFull: Convex domains
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              Text: Nov2025
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