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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: 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 in 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

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: 07/16/2018

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