Related papers: Self adaptive inertial extragradient algorithms fo…
In this paper we consider the variable inequality problem, that is, to find a solution of the inclusion given by the sum of a function and a point-to-cone application. This problem can be seen as a generalization of the classical system…
In a Hilbert setting, we introduce a new dynamical system and associated algorithms for solving monotone inclusions by rapid methods. Given a maximal monotone operator $A$, the evolution is governed by the time dependent operator $I -(I +…
We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…
The Halpern iteration for solving monotone inclusion problems has gained increasing interests in recent years due to its simple form and appealing convergence properties. In this paper, we investigate the inexact variants of the scheme in…
We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…
In this paper we consider iterative methods for stochastic variational inequalities (s.v.i.) with monotone operators. Our basic assumption is that the operator possesses both smooth and nonsmooth components. Further, only noisy observations…
The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…
We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…
In this paper, we introduce three novel splitting algorithms for solving structured monotone inclusion problems involving the sum of a maximally monotone operator, a monotone and Lipschitz continuous operator and a cocoercive operator. Each…
Fixed-point equations with Lipschitz operators have been studied for more than a century, and are central to problems in mathematical optimization, game theory, economics, and dynamical systems, among others. When the Lipschitz constant of…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
We study the convergence issue for the gradient algorithm (employing general step sizes) for optimization problems on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasi-convexity…
In this paper, we propose a multi-step inertial Forward--Backward splitting algorithm for minimizing the sum of two non-necessarily convex functions, one of which is proper lower semi-continuous while the other is differentiable with a…
We propose a hybrid inertial self-adaptive algorithm for solving the split feasibility problem and fixed point problem in the class of demicontractive mappings. Our results are very general and extend several related results existing in…
In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…
We prove non asymptotic total variation estimates for the kinetic Langevin algorithm in high dimension when the target measure satisfies a Poincar\'e inequality and has gradient Lipschitz potential. The main point is that the estimate…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
We propose and analyze an accelerated iterative dual diagonal descent algorithm for the solution of linear inverse problems with general regularization and data-fit functions. In particular, we develop an inertial approach of which we…
In this paper we propose a subgradient algorithm for solving the equilibrium problem where the bifunction may be quasiconvex with respect to the second variable. The convergence of the algorithm is investigated. A numerical example for a…