Related papers: A Proximal-Projection Method for Finding Zeros of …

In this paper, using a new shrinking projection method and generalized resolvents of maximal monotone operators and generalized projections, we consider the strong convergence for finding a common point of the fixed points of a Bregman…

We examine the linear convergence rates of variants of the proximal point method for finding zeros of maximal monotone operators. We begin by showing how metric subregularity is sufficient for linear convergence to a zero of a maximal…

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic $O(1/n)$ convergence rate of our proposed algorithm in…

The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…

We introduce an abstract algorithm that aims to find the Bregman projection onto a closed convex set. As an application, the asymptotic behaviour of an iterative method for finding a fixed point of a quasi Bregman nonexpansive mapping with…

We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…

Proximal operators are now ubiquitous in non-smooth optimization. Since their introduction in the seminal work of Moreau, many papers have shown their effectiveness on a wide variety of problems, culminating in their use to construct…

We study the alternating algorithm for the computation of the metric projection onto the closed sum of two closed subspaces in uniformly convex and uniformly smooth Banach spaces. For Banach spaces which are convex and smooth of power type,…

We introduce and study the convergence properties of a projection-type algorithm for solving the variational inequality problem for point-to-set operators. No monotoni\-city assumption is used in our analysis. The operator defining the…

In this paper, we propose new accelerated methods for smooth convex optimization, called contracting proximal methods. At every step of these methods, we need to minimize a contracted version of the objective function augmented by a…

This paper focuses on a class of inclusion problems of maximal monotone operators in a multi-agent network, where each agent is characterized by an operator that is not available to any other agents, but the agents can cooperate by…

Metric projection operators can be defined in similar wayin Hilbert and Banach spaces. At the same time, they differ signifitiantly in their properties. Metric projection operator in Hilbert space is a monotone and nonexpansive operator. It…

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 introduce a relaxed-projection splitting algorithm for solving variational inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone operators, where the feasible set is defined by a nonlinear and nonsmooth continuous…

This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. The proximal point method includes various well-known convex…

This Note is inspired by the recent paper by Djafary Rouhani and Moradi [J. Optim. Theory Appl. 172 (2017) 222-235], where a proximal point algorithm proposed by Boikanyo and Moro\c{s}anu [Optim. Lett. 7 (2013) 415-420] is discussed. We…

We propose two very simple methods, the first one with constant step sizes and the second one with self-adaptive step sizes, for finding a zero of the sum of two monotone operators in real reflexive Banach spaces. Our methods require only…

In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…

We introduce the first operator splitting method for composite monotone inclusions outside of Hilbert spaces. The proposed primal-dual method constructs iteratively the best Bregman approximation to an arbitrary point from the Kuhn-Tucker…

Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…