A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

Chang, Xiaokai; Liu, Sanyang; Zhao, Pengjun; Song, Dunjiang

doi:10.1016/j.cam.2019.02.028

Cited by 31 publications

(22 citation statements)

References 31 publications

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“…Note that if D k is positive semidefinite, then the above framework is the standard semi-proximal ADMM [30]. However, authors in papers [31]- [33] have also investigated ADMM with the indefinite proximal terms, namely D k is indefinite. The basic principle of choosing D k is to guarantee the convexity of w-subproblem of (22).…”

Section: Framework Of Admmmentioning

confidence: 99%

Support Vector Machine Classifier via Soft-Margin Loss

Wang

Shao

Zhou

et al. 2022

IEEE Trans. Pattern Anal. Mach. Intell.

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Support vector machine (SVM) has attracted great attentions for the last two decades due to its extensive applications, and thus numerous optimization models have been proposed. To distinguish all of them, in this paper, we introduce a new model equipped with an L 0/1 soft-margin loss (dubbed as L 0/1 -SVM) which well captures the nature of the binary classification. Many of the existing convex/non-convex soft-margin losses can be viewed as a surrogate of the L 0/1 soft-margin loss. Despite the discrete nature of L 0/1 , we manage to establish the existence of global minimizer of the new model as well as revealing the relationship among its minimizers and KKT/P-stationary points. These theoretical properties allow us to take advantage of the alternating direction method of multipliers. In addition, the L 0/1 -support vector operator is introduced as a filter to prevent outliers from being support vectors during the training process. Hence, the method is expected to be relatively robust. Finally, numerical experiments demonstrate that our proposed method generates better performance in terms of much shorter computational time with much fewer number of support vectors when against with some other leading methods in areas of SVM. When the data size gets bigger, its advantage becomes more evident.

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Section: Framework Of Admmmentioning

confidence: 99%

Support Vector Machine Classifier via Soft-Margin Loss

Wang

Shao

Zhou

et al. 2022

IEEE Trans. Pattern Anal. Mach. Intell.

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“…Li et al [35] presented a Schur complement based semi-proximal ADMM for convex quadratic conic programming. There are many related studies by incorporating proximal terms into ADMM, we refer the readers to [3,7,9,26,45,47,50]. Recently, He et al [29] proposed an optimal linearized ADMM for solving the two-block problem with the optimal linearization parameter ∈ ( 3 4 , 1) .…”

Section: Introductionmentioning

confidence: 99%

Inertial generalized proximal Peaceman–Rachford splitting method for separable convex programming

Deng

Liu

2021

Calcolo

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The Peaceman-Rachford splitting method (PRSM) is a preferred method for solving the two-block separable convex minimization problems with linear constraints at present. In this paper, we propose an inertial generalized proximal PRSM (abbreviated as IGPRSM) to improve computing efficiency, which unify the ideas of inertial proximal point and linearization technique. Both subproblems are linearized by positive semi-definite proximal matrices, and we explain why the matrix cannot be indefinite. The global convergence and the worst-case asymptotic iteration complexity are derived theoretically via the variational inequality framework. Numerical experiments on LASSO, total variation (TV) based denoising models and image decomposition problems are presented to show the effectiveness of the introduced method even compared with the state-of-the-art methods.

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“…Moreover, Yu [1] introduced the concepts of the order of G(s) and estimated the growth of the maximal molecule M u (σ, G), the maximal term μ(σ, G), the Borel line, and the order of entire functions represented by LaplaceStieltjes transform convergent in the whole complex plane. After his works, considerable attention has been paid to the growth and the value distribution of the functions represented by Lap-laceStieltjes transform convergent in the half plane or whole complex plane in the field of complex analysis (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

Cui

2020

Journal of Function Spaces

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One purpose of this paper is to study the growth of entire functions defined by Laplace-Stieltjes transform converges on the whole complex plane, by introducing the concept of p,q-proximate order, and one equivalence theorem of the p,q-proximate order of Laplace-Stieltjes transforms is obtained. Besides, the second purpose of this paper is to investigate the approximation of entire functions defined by Laplace-Stieltjes transforms with p,q-proximate order, and some results about the p,q-proximate order, the error, and the coefficients of Laplace-Stieltjes transforms are obtained, which are generalization and improvement of the previous theorems given by Luo and Kong, Singhal, and Srivastava.

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A generalization of linearized alternating direction method of multipliers for solving two-block separable convex programming

Cited by 31 publications

References 31 publications

Support Vector Machine Classifier via Soft-Margin Loss

Support Vector Machine Classifier via Soft-Margin Loss

Inertial generalized proximal Peaceman–Rachford splitting method for separable convex programming

Growth and Approximation of Laplace-Stieltjes Transform with p,q-Proximate Order Converges on the Whole Plane

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