Novel Methods for Stochastic Data-Driven Nonconvex Optimization

This project is devoted to the design of new methods for solving high-dimensional, stochastic and non-convex optimization problems, such as those arising in machine learning. The central problem in our investigation is that of training deep neural networks, a notable open problem in the field of numerical optimization and a fundamental building block in a wide range of novel applications including autonomous vehicles, medical diagnosis, and face and speech recognition. Advances in solving this problem will have far reaching impact in other engineering disciplines where new stochastic nonlinear large-scale data-driven models are being developed.