Project Grant 2416250

The National Science Foundation (NSF) awarded a $240,330 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to The Regents of the University of California, doing business as University of California, Berkeley. The grant supports a 2.5-year project to advance state-of-the-art techniques for solving nonconvex optimization problems and games through both theoretical and computational approaches. The core innovation is the concept of "approachable difference-of-convex functions", which aims to uncover a hidden, asymptotically decomposable structure within the multi-composition of nonconvex and non-smooth functions. The project will tackle three main tasks: (i) establishing fundamental properties for this novel class of computationally amenable nonconvex and non-smooth composite functions; (ii) designing and analyzing computational schemes for single-agent optimization problems with objective and constrained functions belonging to this class; and (iii) extending these approaches to address nonconvex games. No subawards are planned under this grant.