Robust Stochastic Optimization The Synergy of Robust Optimization and Stochastic Programming
We present a new mathematical optimization model known as the robust stochastic optimization (RSO) which unifies both stochastic programming and robust optimization in a synergistic and tractable framework that can be solved using the state of the art commercial optimization solvers. The model of uncertainty incorporates both discrete and continuous random variables, typically assumed in stochastic programming and robust optimization respectively. To address the non anticipativity of recourse decisions, we introduce the event wise recourse adaptations, which integrate the scenario tree adaptation originating from stochastic programming and the affine adaptation popularized in robust optimization. Our proposed event wise ambiguity set is rich enough to capture traditional statistic based ambiguity sets such as convex generalized moments, mixture distribution, ph divergence, Wasserstein (Kantorovich Rubinstein) metric, and also opens up novel machine learning based ones such as K means clustering. We also provide several interesting models that are unique in our framework including optimizing over the Hurwicz criterion and portfolio management with adaptive rebalancing. We develop a new algebraic modeling package, RSOME to facilitate implementation of RSO models.