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Chaoyue Zhao (chaoyue.zhaookstate.edu) Abstract: The traditional twostage stochastic program approach is to minimize the total expected cost with the consideration of parameter uncertainty, and the distribution of the random parameters is assumed to be known. However, in most practices, the actual distribution of the random parameters is not known, and only a certain amount of historical data are available. The solution obtained from the traditional twostage stochastic program can be biased and suboptimal for the true problem, if the estimated distribution of the random parameter is not accurate, for which it is usually true when only a limited amount of historical data are available. In this paper, we study the datadriven riskaverse stochastic optimization problem. Instead of assuming the distribution of random parameter is known, a series of historical data, drawn from the true distribution, are observed. Based on the obtained historical data, we construct the confidence set of the ambiguous distribution of the random parameters, and develop a riskaverse stochastic optimization framework to minimize the total expected cost under the worstcase distribution within the constructed confidence set. We introduce the Wasserstein metric to construct the confidence set and by using this metric, we can successfully reformulate the riskaverse twostage stochastic program to its tractable counterpart. In addition, we derive the worstcase distribution and develop efficient algorithms to solve the reformulated problem. Moreover, we perform convergence analysis to show that the riskaverseness of our proposed formulation vanishes as the amount of historical data grows to infinity, and accordingly, the optimal objective value converges to that of the traditional riskneutral twostage stochastic program. Finally, numerical experiments on facility location and stochastic unit commitment problems verify the effectiveness of our proposed solution approach. Keywords: stochastic optimization; datadriven decision making; Wasserstein metric Category 1: Stochastic Programming Citation: Download: [PDF] Entry Submitted: 05/10/2015 Modify/Update this entry  
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