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Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs


P. Mohajerin Esfahani, T. Sutter, J. Lygeros

IEEE Transactions on Automatic Control, vol. 60, no. 1, (arXiv:1307.0345)

We consider the Scenario Convex Program (SCP) for two classes of optimization problems that are not tractable in general: Robust Convex Programs (RCPs) and Chance-Constrained Programs (CCPs). We establish a probabilistic bridge from the optimal value of SCP to the optimal values of RCP and CCP in which the uncertainty takes values in a general, possibly infinite dimensional, metric space. We then extend our results to a certain class of non-convex problems that includes, for example, binary decision variables. In the process, we also settle a measurability issue for a general class of scenario programs, which to date has been addressed by an assumption. Finally, we demonstrate the applicability of our results on a benchmark problem and a problem in fault detection and isolation.

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% Autogenerated BibTeX entry
@Article { EsfSut:2015:IFA_4455,
    author={P. Mohajerin Esfahani and T. Sutter and J. Lygeros},
    title={{Performance Bounds for the Scenario Approach and an
	  Extension to a Class of Non-convex Programs}},
    journal={IEEE Transactions on Automatic Control},
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