Robust Stochastic Optimization With Convex Risk Measures: A Discretized Subgradient Scheme - Yu, H.; Sun, Jie (AMER INST MATHEMATICAL SCIENCES-AIMS, 2021)
We study the distributionally robust stochastic optimization problem within a general framework of risk measures, in which the ambiguity set is described by a spectrum of practically used probability distribution constraints such as bounds on mean-deviation and entropic value-at-risk. We show that a subgradient of the objective function can be obtained by solving a Finite-dimensional optimization problem, which facilitates subgradient-type algorithms for solving the robust stochastic optimization problem. We develop an algorithm for two-stage robust stochastic programming with conditional value at risk measure. A numerical example is presented to show the effectiveness of the proposed method.