Distributionally robust optimization and its applications

点击翻译按钮获取中文摘要

Decisions often need to be made in situations where one has incomplete knowledge about some of the parameters of the problem that he is addressing. This is for example the case in a problem of portfolio selection where the future value of an asset is uncertain, or in an inventory management problem where the future market demand for a product might be subject to changing. Distributionally robust optimization is a generalization of stochastic programming that can provide essential guidance in managing such decision problems since it can account for ambiguity in the choice of a distribution model. Such ambiguity is often present in practice and can make the solution of a stochastic program misleading. The mission of my research program is two-fold. 1) I plan to develop theory that will help answer important open questions that are preventing the distributionally robust model to be applicable at a large scale. 2) I also plan to take a leading role in the integration of the methodology to important industrial problems. These will include: