CRII: CCF: AF: Decomposition Algorithms for nonconvex nonsmooth constrained stochastic programs

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). With the advance of technology, massive, noisy and unstructured data are prevalent in almost every aspect of modern scientific research. It is crucially important to harness big data effectively via more complicated optimization models to make reliable decisions. The handy properties of convexity and smoothness have become the norm of the field traditionally, and the most challenging features of the optimization models, nonconvexity and nondifferentiability, are abandoned and ignored. The pervasiveness of latter properties in the modern science and engineering applications calls for new theory and computational algorithms. Two-stage stochastic programs are optimization models where partial decisions have to be made before the observation of any uncertain parameter, while the remaining decisions are determined after the full information is revealed. This award focuses on designing computational frameworks for large-scale nonconvex and nonsmooth two-stage stochastic programs that are both theoretically rigorous and numerically efficient. The crux of the approach is a novel lifting technique that exposes an implicitly convex-concave structure of the complex value function. The investigator aims to (i) design decomposition schemes and analyze their convergence; and (ii) investigate a fusion of the sampling technique and the decomposition algorithms to accelerate the convergence. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.