Accelerated Inexact Composite Gradient Methods for Nonconvex Spectral Optimization Problems

This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these problems is of the form f_1 + f_2 + h where f_1 and f_2 are differentiable nonconvex matrix functions with Lipschitz continuous gradients, … Read more

An Inexact Spingarn’s Partial Inverse Method with Applications to Operator Splitting and Composite Optimization

We propose and study the iteration-complexity of an inexact version of the Spingarn’s partial inverse method. Its complexity analysis is performed by viewing it in the framework of the hybrid proximal extragradient (HPE) method, for which pointwise and ergodic iteration-complexity has been established recently by Monteiro and Svaiter. As applications, we propose and analyze the … Read more