Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs
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.
Keywords
Cite
@article{arxiv.1307.0345,
title = {Performance Bounds for the Scenario Approach and an Extension to a Class of Non-convex Programs},
author = {Peyman Mohajerin Esfahani and Tobias Sutter and John Lygeros},
journal= {arXiv preprint arXiv:1307.0345},
year = {2014}
}
Comments
19 pages, revised version