In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real Hilbert spaces. Appl...
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In this paper, we propose a novel splitting method for finding a zero point of the sum of two monotone operators where one of them is Lipschizian. The weak convergence the method is proved in real Hilbert spaces. Applying the proposed method to composite monotone inclusions involving parallel sums yields a new primal-dual splitting which is different from the existing methods. Connections to existing works are clearly stated. We also provide an application of the proposed method to the image denoising by the total variation.
In this paper, a regularized dynamical system of forward-backward-forward type method for solving structured monotone inclusions is studied. The novelty of the proposed dynamics consists of the fact that only the alge...
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In this paper, a regularized dynamical system of forward-backward-forward type method for solving structured monotone inclusions is studied. The novelty of the proposed dynamics consists of the fact that only the algebraic part of the dynamical system needs to be regularized, while the differential part remains unchanged. We obtain strong convergence of the generated trajectories to a solution of the original monotone inclusion and under strong monotonicity conditions we obtain a convergence estimate. A time discretization of the dynamical system by explicit Euler scheme provides an iterative regularization forward-backward-forward splitting method with relaxation parameters. Numerical experiments illustrate the effectiveness of the proposed dynamical system approach with regularization.
The paper concerns with three iterative regularization methods for solving a variational inclusion problem of the sum of two operators, the one is maximally monotone and the another is monotone and Lipschitz continuou...
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The paper concerns with three iterative regularization methods for solving a variational inclusion problem of the sum of two operators, the one is maximally monotone and the another is monotone and Lipschitz continuous, in a Hilbert space. We first describe how to incorporate regularization terms in the methods of forward-backward types, and then establish the strong convergence of the resulting methods. With several new stepsize rules considered, the methods can work with or without knowing previously the Lipschitz constant of cost operator. Unlike known hybrid methods, the strong convergence of the proposed methods comes from the regularization technique. Several applications to signal recovery problems and optimal control problems together with numerical experiments are also presented in this paper. Our numerical results have illustrated the fast convergence and computational effectiveness of the new methods over known hybrid methods.
Some extragradient-type algorithms with inertial effect for solving strongly pseudo-monotone variational inequalities have been proposed and investigated recently. While the convergence of these algorithms was establi...
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Some extragradient-type algorithms with inertial effect for solving strongly pseudo-monotone variational inequalities have been proposed and investigated recently. While the convergence of these algorithms was established, it is unclear if the linear rate is guaranteed. In this paper, we provide R-linear convergence analysis for two extragradient-type algorithms for solving strongly pseudo-monotone, Lipschitz continuous variational inequality in Hilbert spaces. The linear convergence rate is obtained without the prior knowledge of the Lipschitz constants of the variational inequality mapping and the stepsize is bounded from below by a positive number. Some numerical results are provided to show the computational effectiveness of the algorithms. (C) 2021 Elsevier B.V. All rights reserved.
We propose two modified Tseng's extragradient methods (also known as forward-backward-forward methods) for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. Under mild a...
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We propose two modified Tseng's extragradient methods (also known as forward-backward-forward methods) for solving non-Lipschitzian and pseudo-monotone variational inequalities in real Hilbert spaces. Under mild and standard conditions, we obtain the weak and strong convergence of the proposed methods. Numerical examples for illustrating the behaviour of the proposed methods are also presented
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