Nonlinear Wasserstein Distributionally Robust Optimization

Professor Yue, Man Chung   (Principal Investigator (PI))

36

2022-01-01

598015

Nonlinear Wasserstein Distributionally Robust Optimization

Distributionally Robust Opt, Geodesic Convex Optimization, Robust Optimization, Infinite-Dim. Optimization, Nonlinear Optimization

Physical Sciences

Physical Sciences (P)

15305321

General Research Fund (GRF) 2021/22

On-going

1. Motivated by its appearance in a wide range of applications and attractive theoretical properties, distributionally robust optimization (DRO) with a Wasserstein ambiguity set and a nonlinear objective in the embedded problem is studied. We call this class of problems nonlinear Wasserstein DRO. Fundamental questions such as optimality conditions, finiteness of the optimal value and existence of optimal solutions to the embedded problem, which is an infinite-dimensional nonlinear constrained optimization over the space of probability distributions, are addressed. 2. Tractable reformulations and approximations for the embedded problem are derived for several classes of well-structured nonlinear functionals of probability distributions that arise from applications. 3. For situations where a tractable reformulation is not available, an iterative algorithm for solving the challenging embedded problem, called the Wasserstein Frank-Wolfe algorithm, is developed. The convergence behavior of the proposed algorithm, such as convergence rate, will be analyzed.