Solving joint chance constrained problems using regularization and Benders' decomposition
Abstract: In this paper we investigate stochastic programs with joint chance constraints. We consider discrete scenario set and reformulate the problem by adding auxiliary variables. Since the resulting problem has a difficult feasible set, we regularize it. To decrease the dependence on the scenario number, we propose a numerical method by iteratively solving a master problem while adding Benders cuts. We find the solution of the slave problem (generating the Benders cuts) in a closed form and propose a heuristic method to decrease the number of cuts. 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 continuous distribution.
Keywords: Stochastic programming; Chance constrained programming; Optimality conditions; Regularization; Benders decomposition; Gas networks
Category 1: Stochastic Programming
Citation: L. Adam, M. Branda, H. Heitsch, R. Henrion: Solving joint chance constrained problems using regularization and Benders' decomposition. Submitted, 2018.
Entry Submitted: 01/06/2018
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