相关论文: A splitting algorithm for fixed points of nonexpan…

We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…

We study the applicability of the Peaceman-Rachford (PR) splitting method for solving nonconvex optimization problems. When applied to minimizing the sum of a strongly convex Lipschitz differentiable function and a proper closed function,…

An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…

We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…

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 extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

We consider the problem of finding the minimizations of the sum of two convex functions and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators,…

We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions…

The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with…

Employing two distinct types of regularization terms, we propose two regularized extragradient methods for solving equilibrium problems on Hadamard manifolds. The sequences generated by these extragradient algorithms converge to a solution…

Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…

In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…

This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…

In this paper, we propose an adaptive forward-backward-forward splitting algorithm for finding a zero of a pseudo-monotone operator which is split as a sum of three operators: the first is continuous single-valued, the second is…

Low rank matrix approximation is a popular topic in machine learning. In this paper, we propose a new algorithm for this topic by minimizing the least-squares estimation over the Riemannian manifold of fixed-rank matrices. The algorithm is…

In this work, a new concept of nonself total asymptotically nonexpansive mapping is introduced and an iterative process is considered for two nonself totally asymptotically nonexpansive mappings. Weak and strong convergence theorems for…

High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…