Relaxed inertial accelerated algorithms for solving split equality feasibility problem

Kao, Xiping; Che, Haitao

doi:10.22436/jnsa.010.08.07

Cited by 10 publications

(10 citation statements)

References 15 publications

(13 reference statements)

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“…Fixing , , the subproblem can be obtained by solving the following minimization problem. Recently, various acceleration techniques of iterative algorithms are proposed [55][56][57][58][59][60][61][62][63]. For this subproblem, in order to accelerate the convergence of the above iteration, we adopt the acceleration technique in [55] to solve it.…”

Section: Alternating Minimization Methodsmentioning

confidence: 99%

Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model

Zhu

Hao

2018

Mathematical Problems in Engineering

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Total variation regularization is well-known for recovering sharp edges; however, it usually produces staircase artifacts. In this paper, in order to overcome the shortcoming of total variation regularization, we propose a new variational model combining high-order total variation regularization and l1 regularization. The new model has separable structure which enables us to solve the involved subproblems more efficiently. We propose a fast alternating method by employing the fast iterative shrinkage-thresholding algorithm (FISTA) and the alternating direction method of multipliers (ADMM). Compared with some current state-of-the-art methods, numerical experiments show that our proposed model can significantly improve the quality of restored images and obtain higher SNR and SSIM values.

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Section: Alternating Minimization Methodsmentioning

confidence: 99%

Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model

Zhu

Hao

2018

Mathematical Problems in Engineering

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“…It is obvious that when θ = , φ θ reduces to the famous CHKS smoothing function, θ = , φ θ reduces to the famous Fischer-Burmeister smoothing function. As we all know, these two smoothing functions and their variants have been widely used in designing smoothing-type methods for solving mathematical programming problems, such as the nonlinear complementarity problems (NCPs) [16][17][18][19][20][21][22], the second-order cone complementarity problems(SOCCPs) [23][24][25][26][27][28][29], the second-order cone programming (SOCP) [30][31][32][33][34][35][36][37][38][39].…”

Section: Smoothing Function and Its Propertiesmentioning

confidence: 99%

A new smoothing method for solving nonlinear complementarity problems

Zhu

Hao

2019

Open Mathematics

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In this paper, a new improved smoothing Newton algorithm for the nonlinear complementarity problem was proposed. This method has two-fold advantages. First, compared with the classical smoothing Newton method, our proposed method needn’t nonsingular of the smoothing approximation function; second, the method also inherits the advantage of the classical smoothing Newton method, it only needs to solve one linear system of equations at each iteration. Without the need of strict complementarity conditions and the assumption of P0 property, we get the global and local quadratic convergence properties of the proposed method. Numerical experiments show that the efficiency of the proposed method.

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“…Nonlinear least squares is an optimization method used to solve nonlinear problems [1][2][3][4]. Sequential quadratic programming is another important and effective optimization method [5][6][7]. A nonlinear least squares problem can be transformed into a sequential quadratic programming model and then solved [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Sequential Quadratic Programming Method for Nonlinear Least Squares Estimation and Its Application

Goulin

Guo

2019

Mathematical Problems in Engineering

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In this study, we propose a direction-controlled nonlinear least squares estimation model that combines the penalty function and sequential quadratic programming. The least squares model is transformed into a sequential quadratic programming model, allowing for the iteration direction to be controlled. An ill-conditioned matrix is processed by our model; the least squares estimate, the ridge estimate, and the results are compared based on a combination of qualitative and quantitative analyses. For comparison, we use two equality indicators: estimated residual fluctuation of different methods and the deviation between estimated and true values. The root-mean-squared error and standard deviation are used for quantitative analysis. The results demonstrate that our proposed model has a smaller error than other methods. Our proposed model is thereby found to be effective and has high precision. It can obtain more precise results compared with other classical unwrapping algorithms, as shown by unwrapping using both simulated and real data from the Jining area in China.

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Relaxed inertial accelerated algorithms for solving split equality feasibility problem

Cited by 10 publications

References 15 publications

Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model

Image Restoration by a Mixed High-Order Total Variation and l1 Regularization Model

A new smoothing method for solving nonlinear complementarity problems

Sequential Quadratic Programming Method for Nonlinear Least Squares Estimation and Its Application

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