In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization prob...In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.展开更多
The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility...The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.展开更多
In this paper,we study the concept of split monotone variational inclusion problem with multiple output sets.We propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solut...In this paper,we study the concept of split monotone variational inclusion problem with multiple output sets.We propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert spaces.Our proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued operators.Moreover,some parameters are relaxed to accommodate a larger range of values for the step sizes.Under some mild conditions on the control parameters and without prior knowledge of the operator norms,we obtain strong convergence result for the proposed method.Finally,we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed method.Several of the existing results in the literature could be viewed as special cases of our result in this paper.展开更多
基金supported by National Research Council of Thailand (NRCT) under grant no. N41A640094the Thailand Science Research and Innovation Fund and the University of Phayao under the project FF66-UoE。
文摘In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.
基金supported by the National Natural Science Foundation of China (11171221)Shanghai Municipal Committee of Science and Technology (10550500800)+1 种基金Basic and Frontier Research Program of Science and Technology Department of Henan Province (112300410277,082300440150)China Coal Industry Association Scientific and Technical Guidance to Project (MTKJ-2011-403)
文摘The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.
基金Supported by National Research Foundation(NRF)of South Africa Incentive Funding for Rated Researchers(Grant No.119903)。
文摘In this paper,we study the concept of split monotone variational inclusion problem with multiple output sets.We propose a new relaxed inertial iterative method with self-adaptive step sizes for approximating the solution of the problem in the framework of Hilbert spaces.Our proposed algorithm does not require the co-coerciveness nor the Lipschitz continuity of the associated single-valued operators.Moreover,some parameters are relaxed to accommodate a larger range of values for the step sizes.Under some mild conditions on the control parameters and without prior knowledge of the operator norms,we obtain strong convergence result for the proposed method.Finally,we apply our result to study certain classes of optimization problems and we present several numerical experiments to demonstrate the implementability of the proposed method.Several of the existing results in the literature could be viewed as special cases of our result in this paper.
