Related papers: An inertial shrinking projection algorithm for spl…
The aim of this paper is to investigate the links between ${\cal T}_C$-class algorithms, CQ Algorithm and shrinking projection methods. We show that strong convergence of these algorithms are related to coherent ${\cal T}_C$-class sequences…
In this paper, using sunny generalized nonexpansive retraction, we propose new extragradient and linesearch algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a…
We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step. The…
In this paper, we use the splitting method to solve support vector machine in reproducing kernel Banach space with lower semi-continuous loss function. We equivalently transfer support vector machines in reproducing kernel Banach space with…
In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are…
This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…
We study the variable metric forward-backward splitting algorithm for convex minimization problems without the standard assumption of the Lipschitz continuity of the gradient. In this setting, we prove that, by requiring only mild…
Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
This work presents a comprehensive discretization theory for abstract linear operator equations in Banach spaces. The fundamental starting point of the theory is the idea of residual minimization in dual norms, and its inexact version using…
Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems that have composite objectives---this already includes the extensively studied convex, composite objective problems as a…
In this paper, we propose a method to approximate the fixed point of an operator in a Banach space. Using biorthogonal systems, this method is applied to build an approximation of the solution of a class of nonlinear partial…
In this paper we study the problems of minimizing the sum of two nonconvex functions: one is differentiable and satisfies smooth adaptable property. The smooth adaptable property, also named relatively smooth condition, is weaker than the…
We introduce two algorithms based on a policy iteration method to numerically solve time-dependent Mean Field Game systems of partial differential equations with non-separable Hamiltonians. We prove the convergence of such algorithms in…
In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and use the theory to obtain convergence results for practical adaptive…
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…
Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, an inexact projected gradient method for solving smooth constrained vector optimization problems on…
In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving a variational inequality problem with a monotone and Lipschitz continuous operator in…
The paper considers a split inverse problem involving component equilibrium problems in Hilbert spaces. This problem therefore is called the split equilibrium problem (SEP). It is known that almost solution methods for solving problem (SEP)…
Constructing or learning a function from a finite number of sampled data points (measurements) is a fundamental problem in science and engineering. This is often formulated as a minimum norm interpolation problem, regularized learning…