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

P. Mohajerin Esfahani, Tobias Sutter, John Lygeros

Research output: Contribution to journalArticleScientificpeer-review

46 Citations (Scopus)

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.

Original languageEnglish
Article number6832537
Pages (from-to)46-58
JournalIEEE Transactions on Automatic Control
Volume60
Issue number1
DOIs
Publication statusPublished - 2015
Externally publishedYes

Bibliographical note

Op verzoek van PM Esfahani geregistreerd in Pure vanwege een aanvraag in het kader van het H2020-programma. door het ontbreken van de TU Delft affiliatie geen research output van de TU Delft.

Keywords

  • Chance-constrained programs
  • performance bound
  • randomized algorithm
  • scenario program
  • semi-infinite programming
  • uncertain convex optimization

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