Related papers: An inertial Tseng's type proximal algorithm for no…
In this paper, we study an algorithm for solving a class of nonconvex and nonsmooth nonseparable optimization problems. Based on proximal alternating linearized minimization (PALM), we propose a new iterative algorithm which combines…
In this paper we aim to minimize the sum of two nonsmooth (possibly also nonconvex) functions in separate variables connected by a smooth coupling function. To tackle this problem we chose a continuous forward-backward approach and…
This work investigates a Bregman and inertial extension of the forward-reflected-backward algorithm [Y. Malitsky and M. Tam, SIAM J. Optim., 30 (2020), pp. 1451--1472] applied to structured nonconvex minimization problems under relative…
The classical Krasnoselskii-Mann iteration is broadly used for approximating fixed points of nonexpansive operators. To accelerate the convergence of the Krasnoselskii-Mann iteration, the inertial methods were received much attention in…
In this paper we introduce a novel abstract descent scheme suited for the minimization of proper and lower semicontinuous functions. The proposed abstract scheme generalizes a set of properties that are crucial for the convergence of…
In this paper we present an abstract convergence analysis of inexact descent methods in Riemannian context for functions satisfying Kurdyka-Lojasiewicz inequality. In particular, without any restrictive assumption about the sign of the…
We propose BIBPA, a block inertial Bregman proximal algorithm for minimizing the sum of a block relatively smooth function (that is, relatively smooth concerning each block) and block separable nonsmooth nonconvex functions. We prove that…
We propose an inertial variant of the strongly convergent inexact proximal-point (PP) method of Solodov and Svaiter (2000) for monotone inclusions. We prove strong convergence of our main algorithm under less restrictive assumptions on the…
Nonconvex and nonsmooth optimization problems are important and challenging for statistics and machine learning. In this paper, we propose Projected Proximal Gradient Descent (PPGD) which solves a class of nonconvex and nonsmooth…
Inertial algorithms for minimizing nonsmooth and nonconvex functions as the inertial proximal alternating linearized minimization algorithm (iPALM) have demonstrated their superiority with respect to computation time over their non inertial…
This work considers an Inertial version of Bregman Proximal Gradient algorithm (IBPG) for minimizing the sum of two single-valued functions in finite dimension. We suppose that one of the functions is proper, closed, and convex but…
In view of the minimization of a function which is the sum of a differentiable function $f$ and a convex function $g$ we introduce descent methods which can be viewed as produced by inexact auxiliary problem principleor inexact variable…
We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
We consider the composite minimization problem with the objective function being the sum of a continuously differentiable and a merely lower semicontinuous and extended-valued function. The proximal gradient method is probably the most…
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or {\L}ojasiewicz properties. These geometrical notions are usually local by nature, and may…
In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…
We propose inertial versions of block coordinate descent methods for solving non-convex non-smooth composite optimization problems. Our methods possess three main advantages compared to current state-of-the-art accelerated first-order…
We consider a composite optimization problem where the sum of a continuously differentiable and a merely lower semicontinuous function has to be minimized. The proximal gradient algorithm is the classical method for solving such a problem…