Probabilistic feasibility guarantees for convex scenario programs with an arbitrary number of discarded constraints

Journal article

Discarding constraints in scenario optimization, a technique known as the sampling-and-discarding scheme, allows the decision maker to trade feasibility to performance. Recently, a removal scheme with a less conservative bound on the constraint violation probability of the final decision has been proposed. In this letter, we further contribute to the theoretical properties of such a scheme by extending the number of discarded scenarios to be arbitrary, as opposed to an integer multiple of the dimension of the decision space. There are two facets to the results of this paper. On the one hand, our feasibility guarantees outperform the standard “sampling-and-discarding” bound in the literature. On the other hand, we highlight an inherent property of the discarding mechanism, namely, the fact that removing a number of scenarios that is not an integer multiple of the dimension of the decision space is likely to introduce additional conservatism.

Authors: Romao, L; Margellos, KN; Papachristodoulou, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Automatica
• Volume: 149
• Article number: 110601
• Publication date: 2023-01-12
• Acceptance date: 2022-06-15
• DOI: 10.1016/j.automatica.2022.110601
• ISSN: 0005-1098
• Language: English
• Keywords: FFR