In this work, we propose some new douglas-Rashford splittingalgorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal propert...
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In this work, we propose some new douglas-Rashford splittingalgorithms for solving a class of generalized DC (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth component and a fasten control parameter which improves the convergence rate of the algorithms. We prove the convergence of these methods to the critical points of nonconvex optimization under reasonable conditions. We evaluate the performance and effectiveness of our methods through experimentation with three practical examples in machine learning. Our findings demonstrated that our methods offer efficiency in problem-solving and outperform state-of-the-art techniques like the DCA (DC algorithm) and ADMM.
The Canonical Polyadic Decomposition (CPD) is the tensor analog of the Singular Value Decomposition (SVD) for a matrix and has many data science applications including signal processing and machine learning. For the C...
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The Canonical Polyadic Decomposition (CPD) is the tensor analog of the Singular Value Decomposition (SVD) for a matrix and has many data science applications including signal processing and machine learning. For the CPD, the Alternating Least Squares (ALS) algorithm has been used extensively. Although the ALS algorithm is simple, it is sensitive to a noise of a data tensor in the applications. In this paper, we propose a novel strategy to realize the noise suppression for the CPD. The proposed strategy is decomposed into two steps: (Step 1) denoising the given tensor and (Step 2) solving the exact CPD of the denoised tensor. Step 1 can be realized by solving a structured low-rank approximation with the douglas-rachford splitting algorithm and then Step 2 can be realized by solving the simultaneous diagonalization of a matrix tuple constructed by the denoised tensor with the DODO method. Numerical experiments show that the proposed algorithm works well even in typical cases where the ALS algorithm suffers from the so-called bottleneck/swamp effect.
This paper is devoted to the optimal selection of the relaxation parameter sequence for Krasnosel'ski-Mann iteration. Firstly, we establish the optimal relaxation parameter sequence of the Krasnosel'ski-Mann i...
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This paper is devoted to the optimal selection of the relaxation parameter sequence for Krasnosel'ski-Mann iteration. Firstly, we establish the optimal relaxation parameter sequence of the Krasnosel'ski-Mann iteration, with which the algorithm is proved to achieve the optimal convergence rate. Then we present an approximation to the optimal relaxation parameter sequence since the optimal relaxation parameter sequence involves fixed points of the operators and can't be used in actual computing. Thirdly, we apply our results to the operators splitting method, such as forward-backward splitting methods and douglas-rachfordsplitting method. Finally, numerical experiments are provided to illustrate that Krasnosel'ski-Mann iteration and the relaxed projected method with our proposed relaxation parameter sequence behave better than others.
This paper proposes a new model to remove the multiplicative noise. We incorporate the cartoon-texture decomposition into a multiplicative denoising model, and design a new convex optimization model. The superiority o...
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ISBN:
(纸本)9781509035885
This paper proposes a new model to remove the multiplicative noise. We incorporate the cartoon-texture decomposition into a multiplicative denoising model, and design a new convex optimization model. The superiority of the proposed model lies in adding the H-1 norm of texture component, which can help to recover more image information. We solve the model numerically by douglas-rachford splitting algorithm and the Fourier domain filtering. Experimental results show that the designed algorithms can solve the model effectively, the recovery images of the new model have better visual quality, and also have higher signal to noise ratios and peak signal to noise ratios.
The alternating direction method of multipliers(ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving ...
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The alternating direction method of multipliers(ADMM) is a widely used method for solving many convex minimization models arising in signal and image processing. In this paper, we propose an inertial ADMM for solving a two-block separable convex minimization problem with linear equality constraints. This algorithm is obtained by making use of the inertial douglas-rachford splitting algorithm to the corresponding dual of the primal problem. We study the convergence analysis of the proposed algorithm in infinite-dimensional Hilbert ***, we apply the proposed algorithm on the robust principal component analysis problem and also compare it with other state-of-the-art algorithms. Numerical results demonstrate the advantage of the proposed algorithm.
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