A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem

Tao, Pham Dinh; Thi, Hoai An Le

doi:10.1137/s1052623494274313

Cited by 468 publications

(140 citation statements)

References 21 publications

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“…This confirms the observations of Tao and An (1998) whereby DCA converges to "good" local minima, and often to global minima in practice.…”

Section: Last Vs Stochastic Gradient Descentsupporting

confidence: 87%

“…DCA is an iterative algorithm that consists in solving, at each iteration, the convex optimization problem obtained by linearizing h (i.e., the non convex part of f = g − h) around the current solution. The local convergence of DCA is proven in Theorem 3.7 of Tao and An (1998), and we refer to this paper for further theoretical guarantees on the stability and robustness of the algorithm. Although DCA is only guaranteed to reach a local minima, the authors of Tao and An (1998) state that DCA often converges to a global optimum.…”

Section: Optimizationmentioning

confidence: 99%

“…The local convergence of DCA is proven in Theorem 3.7 of Tao and An (1998), and we refer to this paper for further theoretical guarantees on the stability and robustness of the algorithm. Although DCA is only guaranteed to reach a local minima, the authors of Tao and An (1998) state that DCA often converges to a global optimum. When this is not the case, using multiple restarts might be used to improve the solution.…”

Section: Optimizationmentioning

confidence: 99%

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Dictionary Learning for Fast Classification Based on Soft-thresholding

2014

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Classifiers based on sparse representations have recently been shown to provide excellent results in many visual recognition and classification tasks. However, the high cost of computing sparse representations at test time is a major obstacle that limits the applicability of these methods in large-scale problems, or in scenarios where computational power is restricted. We consider in this paper a simple yet efficient alternative to sparse coding for feature extraction. We study a classification scheme that applies the soft-thresholding nonlinear mapping in a dictionary, followed by a linear classifier. A novel supervised dictionary learning algorithm tailored for this low complexity classification architecture is proposed. The dictionary learning problem, which jointly learns the dictionary and linear classifier, is cast as a difference of convex (DC) program and solved efficiently with an iterative DC solver. We conduct experiments on several datasets, and show that our learning algorithm that leverages the structure of the classification problem outperforms generic learning procedures. Our simple classifier based on soft-thresholding also competes with the recent sparse coding classifiers, when the dictionary is learned appropriately. The adopted classification scheme further requires less computational time at the testing stage, compared to other classifiers. The proposed scheme shows the potential of the adequately trained soft-thresholding mapping for classification and paves the way towards the development of very efficient classification methods for vision problems.

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“…This confirms the observations of Tao and An (1998) whereby DCA converges to "good" local minima, and often to global minima in practice.…”

Section: Last Vs Stochastic Gradient Descentsupporting

confidence: 87%

Section: Optimizationmentioning

confidence: 99%

Section: Optimizationmentioning

confidence: 99%

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Dictionary Learning for Fast Classification Based on Soft-thresholding

2014

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“…Since the matrix K of these examples can be diagonalized by Fourier transform, therefore our algorithms can be effectively carried out. We compare our methods with 1 l [14], 12 ll − [3], and 12 ll α − [4]. In order to verify the proposed methods thoroughly, we use 14 test images from [15] including synthesis images and natural images which are shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

“…DCA is appropriate when the objective function can be decoupled into difference of two convex functions, therefore, we employ the DCA to solve our model. Tao and An proposed DCA [11,12] In what follows, we briefly review the SBI for the sake of completeness. The SBI is useful when 1 l minimization problem is following form 1 =||()||() argmin uuEu φ + (10) where E and φ are convex.…”

Section: Related Workmentioning

confidence: 99%

Hybrid Model and Split Bregman Iteration Algorithm for Image Denoising

Yu¹,

Zhang²

2018

Proceedings of the 2nd International Forum on Management, Education and Information Technology Application (IFMEITA 2017)

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Keywords: hybrid model; difference of convex algorithm; split Bregman iteration; image denoising. Abstract.Although difference of convex model has attracted many research efforts due to its superior performance for image processing, no attention has focused on robust data fidelity for this model. In this paper, we propose a novel model, which combines the 1 l and 2 l fidelity terms with a weighted difference of anisotropic and isotropic total variation (TV). Since our model takes a new difference form of convex terms, we employ difference of convex algorithm (DCA). In this paper, we adopt split Bregman iteration (SBI) to solve each DCA subproblem of the proposed model. Image denoising verifies the convergence of optimal solution and monotone decreasing of objective function. Experimental results on image denoising demonstrate that the proposed methods outperform other competing methods in terms of quantitative criteria and perceptual quality.

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Large Scale Trust Region Problems

Palagi

2001

Encyclopedia of Optimization

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A D.C. Optimization Algorithm for Solving the Trust-Region Subproblem

Cited by 468 publications

References 21 publications

Dictionary Learning for Fast Classification Based on Soft-thresholding

Dictionary Learning for Fast Classification Based on Soft-thresholding

Hybrid Model and Split Bregman Iteration Algorithm for Image Denoising

Large Scale Trust Region Problems

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