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Pareto efficiency for robust linear programs was introduced by Iancu and Trichakis in [Manage Sci 60(1):130–147, 9]. We generalize their approach and theoretical results to robust optimization problems in Euclidean spaces with affine uncertainty. Additionally, we demonstrate the value of this approach in an exemplary manner in the area of robust semidefinite programming (SDP). In particular, we prove that computing a Pareto robustly optimal solution for a robust SDP is tractable and illustrate the benefit of such solutions at the example of the maximal eigenvalue problem. Furthermore, we modify the famous algorithm of Goemans and Williamson [Assoc Comput Mach 42(6):1115–1145, 8] in order to compute cuts for the robust max-cut problem that yield an improved approximation guarantee in... |
The guide curves are tools that specify rules for dam operation that allow reducing the chances of unwanted spill or deficit events. In this research, we analyzed the importance of using guide curves and penalizing the deviation of such curves by the occurrence of surplus volume, or deficit, using optimization tools on an objective function that apply stochastic dynamic programming (SDP), guide curves and reservoir operation simulation all together, to obtain and evaluate biweekly operation policies for hydropower generation purposes. The main dams of the Grijalva River were taken as a case study. The optimization tool is based on sequential decision stages (time intervals) to operate a dam system that considers the restrictions on storage volumes, defined by high and low guide curv... |
