Jianqiang Cheng (U Arizona) Approximated Distributionally Robust Optimization

Distributionally robust optimization (DRO) has gained increasing popularity because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being theoretically solvable in polynomial time, SDP problems in practice are computationally challenging and quickly become intractable with increasing problem size. In this talk, we present computationally efficient
(inner and outer) approximations for DRO problems based on the idea of dimensionality reduction techniques. We also derive theoretical bounds on the gaps between the original problem and its approximations. Furthermore, an extensive numerical study, including an application in power systems, shows the strength of the proposed approximations in terms of solution quality and runtime.

distributionally robust optimization,PCA,Moment Ambiguity,Wasserstein Ambiguity,Approximation Algorithm and Bounds,