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arXiv · 1307.0345

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

Peyman Mohajerin Esfahani·Tobias Sutter·John Lygeros
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Abstract

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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Peyman Mohajerin Esfahani, Tobias Sutter, John Lygeros. 2013-07-01. Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs. https://doi.org/10.1109/tac.2014.2330702

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