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Solving joint chance constrained problems using regularization and Benders' decomposition
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DOI：10.1007/s10479-018-3091-9.png)
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Abstract
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We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by iteratively solving a master problem while adding Benders' cuts from a slave problem. Since the number of variables of the slave problem equals to the number of scenarios, we express its solution in a closed form. We show convergence properties of the solutions. On a gas network design problem, we perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with the continuous distribution.
Keywords:
Stochastic programming
Chance constrained programming
Optimality conditions
Regularization
Benders' decomposition
Gas networks
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