Search

In this study, we suggest a new class of forward-backward (FB) algorithms designed to solve convex minimization problems. Our method incorporates a linesearch technique, eliminating the need to choose Lipschitz assumptions explicitly. Additionally, we apply double inertial extrapolations to enhance the algorithm's convergence rate. We establish a weak convergence theorem under some mild conditions. Furthermore, we perform numerical tests, and apply the algorithm to image restoration and data classification as a practical application. The experimental results show our approach's superior performance and effectiveness, surpassing some existing methods in the literature.

Abstract In this paper, we propose two inertial algorithms with a new self-adaptive step size for approximating a solution of the split common null-point problem in the framework of Banach spaces. The step sizes are adaptively updated over each iteration by a simple process without the prior knowledge of the operator norm of the bounded linear operator. Under suitable conditions, we prove the weak-convergence results for the proposed algorithms in p-uniformly convex and uniformly smooth Banach spaces. Finally, we give several numerical results in both finite- and infinite-dimensional spaces to illustrate the efficiency and advantage of the proposed methods over some existing methods. Also, data classifications of heart diseases and diabetes mellitus are presented as the applications of our methods.

In this paper, the aim is to design a new proximal gradient algorithm by using the inertial technique with adaptive stepsize for solving convex minimization problems and prove convergence of the iterates under some suitable assumptions. Some numerical implementations of image deblurring are performed to show the efficiency of the proposed methods.

In this work, we propose a new relaxed projection algorithm for the split feasibility problem with a new linesearch. The proposed method does not require the computation on the matrix inverse and the largest eigenvalue of the matrix. We then prove some weak convergence theorems under suitable conditions in the framework of Hilbert spaces. Finally, we give some numerical examples in signal processing to validate the theoretical analysis results. The obtained results improve the corresponding results in the literature.

We designed a modified projection method with a new condition of the inertial step and the step size for the split feasibility problem in Hilbert spaces. We show that our iterate weakly converged to a solution. Lastly, we give numerical examples and comparisons that could be applied to signal recovery to show the efficiency of our method.

We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences.

In this paper, we focus on studying the split feasibility problem (SFP), which has many applications in signal processing and image reconstruction. A popular technique is to employ the iterative method which is so called the relaxed CQ algorithm. However, the speed of convergence usually depends on the way of selecting the step size of such algorithms. We aim to suggest a new hybrid CQ algorithm for the SFP by using the self adaptive and the line-search techniques. There is no computation on the inverse and the spectral radius of a matrix. We then prove the weak convergence theorem under mild conditions. Numerical experiments are included to illustrate its performance in compressed sensing. Some comparisons are also given to show the efficiency with other CQ methods in the literature.

In this work, we study the inclusion problem of the sum of two monotone operators and the fixed-point problem of nonexpansive mappings in Hilbert spaces. We prove the weak and strong convergence theorems under some weakened conditions. Some numerical experiments are also given to support our main theorem.

In this paper, we propose a new method for solving variational inclusion problems in Hilbert spaces. This algorithm uses two inertial terms to speed up the convergence. In order to avoid computing the Lipschitz stepsize, we use an updated stepsize which is not necessary to know the Lipschitz constant of the operator. The weak convergence is established under some mild conditions. We present numerical performance of the proposed algorithm and compare our algorithm with other algorithms in literature. Finally, we deduce our algorithm for solving the convex minimization problem and give an application to the data classification problem of heart failure dataset. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the convex minimization problem in real Hilbert spaces. We introduce a new relaxed forward-backward-forward method by using the inertial technique and the adaptive stepsize. We then provide its convergence theorem under suitable assumptions. Finally, we analyse the proposed method to image inpainting and give comparisons of our method with other methods in the literature. [ABSTRACT FROM AUTHOR]