On the convergence of cutting-plane methods for robust optimization with ellipsoidal uncertainty sets

2019/04/02 by Mínguez, Roberto, Casero-Alonso, Víctor
#Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #and Science (cs.CE)

paper · doi:10.48550/arxiv.1904.01244

Abstract

Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral uncertainty sets guarantees convergence, finite termination when using ellipsoidal uncertainty sets is not theoretically guaranteed. This paper demonstrates that the cutting-plane algorithm set out for ellipsoidal uncertainty sets in its more general form also converges in a finite number of steps.

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