Accelerated Inexact First-Order Methods for Solving Nonconvex Composite Optimization Problems

Weiwei Kong

Abstract: This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. Our main tools mainly come from variational and convex analysis, and our key results are in the form of iteration complexity bounds and how these bounds compare to other ones in the literature.