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Solving joint chance constrained problems using regularization and Benders' decomposition

Lukas Adam(adam***at***utia.cas.cz)
Martin Branda(branda***at***utia.cas.cz)
Holger Heitsch(heitsch***at***wias-berlin.de)
Rene Henrion(henrion***at***wias-berlin.de)

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.

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Entry Submitted: 01/06/2018
Entry Accepted: 01/08/2018
Entry Last Modified: 01/06/2018

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