Methods for High-Dimensional Nonlinear Optimization

High-dimensional, nonlinear, stochastic optimization problems arise in a wide variety of data science applications. We propose a general algorithmic framework that takes advantage of the stochastic nature of the objective function and can exploit parallelism. The proposed methods scale into the millions of variables by employing sampling and sketching techniques. Adaptive scaling methods for solving non-convex optimization problems will also be developed, together with new measures for characterizing robust solutions.