Inertial Block Mirror Descent Method for Non-Convex Non-Smooth Optimization

In this paper, we propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. We use the general framework of Bregman distance functions to compute the proximal maps. Our method not only allows using two different extrapolation points to evaluate gradients and adding the inertial force, but also takes advantage … Read more

Forward-backward truncated Newton methods for convex composite optimization

This paper proposes two proximal Newton-CG methods for convex nonsmooth optimization problems in composite form. The algorithms are based on a a reformulation of the original nonsmooth problem as the unconstrained minimization of a continuously differentiable function, namely the forward-backward envelope (FBE). The first algorithm is based on a standard line search strategy, whereas the … Read more