We present a Julia computational toolbox for linear optimization problems with joint affine chance constraints under elliptically symmetric uncertainty. The toolbox combines a spherical–radial oracle for estimating the joint probability and its gradient with three structured optimization methods: Proximal, Feasible, and Penalty. The oracle supports several elliptically symmetric distributions and is integrated with these methods through a common computational interface. Interfaces to a level-bundle method and \textsc{IPOPT} are also provided for comparison. Under suitable regularity assumptions, the structured methods satisfy their respective convergence guarantees, and feasible critical points satisfy the Karush–Kuhn–Tucker (KKT) conditions under an appropriate constraint qualification. Numerical experiments on cash-matching, transportation, and realistic hydro-valley problems under Gaussian and Student-$t$ uncertainty assess computational time, probability-oracle evaluations, and sensitivity to initialization. The results show that the structured methods are generally more efficient and robust than the benchmark approaches across the tested problem classes.
A Computational Toolbox for Linear Optimization with Joint Affine Chance Constraints
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