We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite data-set, according to the scenario robust optimization paradigm. By exploiting the structure of the constraints, we show that both a priori and a posteriori distribution-free probabilistic robustness certificates for a possibly sub-optimal solution to the resulting data-driven optimization problem can be obtained with minimal computational effort. Building on these results, we also discuss a one-shot and an incremental procedure to determine the size of the data-set so as to guarantee a user-chosen robustness level. Notably, both the a posteriori robustness assessment and incremental data-set sizing do not require to solve the non-convex scenario program. A comparative analysis performed on the unit commitment problem using real data reveals a limited increase in conservativeness with a significant computational saving with respect to the application of scenario theory results for general, non necessarily structured, non-convex problems.
Scenario optimization with certificates and applications to anti-windup design
Politecnico di Milano（米兰理工大学）；CNRS, LAAS（法国国家科学研究中心，图卢兹实验室）；Univ. de Toulouse, LAAS（图卢兹大学，图卢兹实验室）；Dip. di Ingegneria Industriale, University of Trento（特伦托大学工业工程系）；CNR-IEIIT（意大利国家研究委员会信息技术研究所）
Scenario theory for multi-criteria data-driven decision making
Dipartimento di Elettronica Informazione e Bioingegneria, Politecnico di Milano（米兰理工大学电子、信息与生物工程系）；Dipartimento di Ingegneria dell’Informazione, Università degli studi di Brescia（布雷西亚大学信息工程系）
