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
Published Version
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