This paper concerns with efficient projection onto the ordered weighted l_(1)norm ball,which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine subsp...This paper concerns with efficient projection onto the ordered weighted l_(1)norm ball,which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine subspace.Based on Lagrangian relaxation and secant approximation method,we propose an easily implementable yet efficient algorithm to solve the projection problem which is proved to terminate after a finite number of iterations.Furthermore,we design efficient implementations for our algorithm and compare it with a semismooth Newton(SSN)algorithm and a root-finding(Root-F)algorithm.Numerical results on a diversity of test problems show that our algorithm is superior than SSN and Root-F.展开更多
In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minim...In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.展开更多
In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed f...In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.展开更多
In this papert the matrix of equidiagonal-dominance is defined and several theorems about ||A-1||∞ and its evaluation are established. Many interesting numerical examples are given.
基金supported by the National Natural Science Foundation of China(No.11871153)the Natural Science Foundation of Fujian Province of China(No.2019J01644).
文摘This paper concerns with efficient projection onto the ordered weighted l_(1)norm ball,which is equivalent to the problem of finding projector onto the intersection of the monotone nonnegative cone and an affine subspace.Based on Lagrangian relaxation and secant approximation method,we propose an easily implementable yet efficient algorithm to solve the projection problem which is proved to terminate after a finite number of iterations.Furthermore,we design efficient implementations for our algorithm and compare it with a semismooth Newton(SSN)algorithm and a root-finding(Root-F)algorithm.Numerical results on a diversity of test problems show that our algorithm is superior than SSN and Root-F.
基金supported by the National Natural Science Foundation of China under grants U21A20455,61972265,11871348 and 11701388by the Natural Science Foundation of Guangdong Province of China under grant 2020B1515310008by the Educational Commission of Guangdong Province of China under grant 2019KZDZX1007.
文摘In recent years,the nuclear norm minimization(NNM)as a convex relaxation of the rank minimization has attracted great research interest.By assigning different weights to singular values,the weighted nuclear norm minimization(WNNM)has been utilized in many applications.However,most of the work on WNNM is combined with the l 2-data-fidelity term,which is under additive Gaussian noise assumption.In this paper,we introduce the L1-WNNM model,which incorporates the l 1-data-fidelity term and the regularization from WNNM.We apply the alternating direction method of multipliers(ADMM)to solve the non-convex minimization problem in this model.We exploit the low rank prior on the patch matrices extracted based on the image non-local self-similarity and apply the L1-WNNM model on patch matrices to restore the image corrupted by impulse noise.Numerical results show that our method can effectively remove impulse noise.
基金supported by National Natural Science Foundation of China(Grant No.11901107)the Young Elite Scientists Sponsorship Program by CAST(Grant No.2019QNRC001)+1 种基金the Shanghai Sailing Program(Grant No.19YF1402600)the Science and Technology Commission of Shanghai Municipality Project(Grant No.19511120700).
文摘In this paper,we provide a finitely terminated yet efficient approach to compute the Euclidean projection onto the ordered weightedℓ_(1)(OWL1)norm ball.In particular,an efficient semismooth Newton method is proposed for solving the dual of a reformulation of the original projection problem.Global and local quadratic convergence results,as well as the finite termination property,of the algorithm are proved.Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.In addition,we derive the generalized Jacobian of the studied projector which,we believe,is crucial for the future designing of fast second-order nonsmooth methods for solving general OWL1 norm constrained problems.
文摘In this papert the matrix of equidiagonal-dominance is defined and several theorems about ||A-1||∞ and its evaluation are established. Many interesting numerical examples are given.
