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Using the scenario approach for chance constrained optimization problems


K. Margellos

IfA Internal Seminar Series

This talk deals with a new method for solving chance constrained optimization problems which lies between robust optimization and scenario-based methods. The proposed approach does not require prior knowledge of the underlying probability distribution as in standard robust optimization methods, nor is it based entirely on randomization as in the scenario approach. It instead involves solving a robust optimization problem with bounded uncertainty, where the uncertainty bounds are randomized and are computed using the scenario approach. Specifically, we provide two alternatives to the standard scenario approach and show that for a given performance level, the number of scenarios is not proportional to the number of decision variables as in the scenario approach, but is proportional to the dimension of the uncertainty vector or the number of constraints respectively. The proposed solution methods are compared with the scenario approach by means of numerical examples.


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J. Lygeros

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