Robust Optimization (RO) is an approach to tackle uncertainties in the parameters of an optimization problem. Constructing an uncertainty set is crucial for RO, as it determines the quality and the conservativeness of the solutions. In this paper, we introduce an approach for constructing a data-driven uncertainty set through volume-based clustering, which we call Minimum-Volume … Read more
This study proposes a mathematical optimization programming model that simultaneously forecasts interest rate market scenarios and significant losses on interest rate market portfolios. The model includes three main components. A constraint condition is set using the Mahalanobis distance, which consists of innovation terms in a dynamic conditional correlation-generalized autoregressive conditional heteroscedasticity (DCC-GARCH) model that represent … Read more
We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven robust optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of robust optimization problems. The induced robust counterpart problem retains the … Read more
We propose a framework for sensitivity analysis of linear programs (LPs) in minimiza- tion form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact, convex uncertainty set. This framework unifies and extends multiple approaches for LP sensitivity analysis in the literature and has close ties … Read more