Revealing Determination Conservativeness By way of Inverse Distributionally Strong Optimization
Authors: Qi Li, Zhirui Liang, Andrey Bernstein, Yury Dvorkin
Summary: This paper introduces Inverse Distributionally Strong Optimization (I-DRO) as a technique to deduce the conservativeness stage of a decision-maker, represented by the dimensions of a Wasserstein metric-based ambiguity set, from the optimum choices made utilizing Ahead Distributionally Strong Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) situations of the convex F-DRO mannequin, we formulate I-DRO as a bi-linear program, which will be solved utilizing off-the-shelf optimization solvers. Moreover, this formulation reveals a number of advantageous properties. We show that I-DRO not solely ensures the existence and uniqueness of an optimum answer but additionally establishes the required and enough situations for this optimum answer to precisely match the precise conservativeness stage in F-DRO. Moreover, we determine three excessive eventualities which will impression I-DRO effectiveness. Our case research applies F-DRO for energy system scheduling beneath uncertainty and employs I-DRO to get better the conservativeness stage of system operators. Numerical experiments based mostly on an IEEE 5-bus system and a sensible NYISO 11-zone system show I-DRO efficiency in each regular and excessive eventualities.