Regularization methods are a key tool in the solution of inverse problems. They are used to
introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses …

Backtracking line-search is an old yet powerful strategy for finding better step sizes to be
used in proximal gradient algorithms. The main principle is to locally find a simple convex …

We study convergence rates of the classic proximal bundle method for a variety of
nonsmooth convex optimization problems. We show that, without any modification, this …

We introduce Bella, a locally superlinearly convergent Bregman forward-backward splitting
method for minimizing the sum of two nonconvex functions, one of which satisfies a relative …

We consider optimization methods for convex minimization problems under inexact
information on the objective function. We introduce inexact model of the objective, which as …

We introduce a framework for quasi-Newton forward-backward splitting algorithms (proximal
quasi-Newton methods) with a metric induced by diagonal ± rank-r symmetric positive …

In this paper, we propose a general algorithmic framework for the first-order methods in
optimization in a broad sense, including minimization problems, saddle-point problems and …

We consider optimization algorithms that successively minimize simple Taylor-like models of
the objective function. Methods of Gauss–Newton type for minimizing the composition of a …

This paper proposes an inertial Bregman proximal gradient method for minimizing the sum
of two possibly nonconvex functions. This method includes two different inertial steps and …

Finding stationary states of Landau free energy functionals has to solve a nonconvex infinite-
dimensional optimization problem. In this paper, we develop a Bregman distance based …