Data-driven two-stage distributionally robust optimization with risk aversion

Abstract

This paper studies a two-stage distributionally robust optimization problem with risk aversion. We define an ambiguity set containing the true distribution function with L1 distance. Taking a data-driven approach, we use a product kernel density to estimate the nominal distribution and provide the bounds of the estimation. For tractability, we transform the worst-case risk aversion problem into a linear programming problem. To handle the risk measure in the objective function, we propose a modified decomposition method. Numerical tests are utilized to validate the proposed method.