Results 11 to 20 of about 510 (73)
A Modified Approach to Distributed Bregman ADMM for a Class of Nonconvex Consensus Problems
Journal of MathematicsThis article presents a refined iteration of the distributed Bregman alternating direction method of multipliers (ADMM) tailored to tackle nonconvex consensus issues, especially those with multiple blocks.
Zhonghui Xue, Qianfeng Ma, Yazheng Dang
doaj +2 more sources
Convergence Analysis of Multiblock Inertial ADMM for Nonconvex Consensus Problem
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 The alternating direction method of multipliers (ADMM) is one of the most powerful and successful methods for solving various nonconvex consensus problem. The convergence of the conventional ADMM (i.e., 2‐block) for convex objective functions has been stated for a long time.
Yang Liu, Yazheng Dang, Qiang Wu
wiley +1 more source
Non‐convex nonlocal adaptive tight frame image deblurring
IET Image Processing, Volume 16, Issue 7, Page 1908-1923, 29 May 2022., 2022 Abstract The challenge of the image restoration is to recover more detailed information from the degraded images. Based on the observations that wavelet frames have efficient representation ability to image details and the nonconvex regularization in the model may admit unbiased solutions, in this paper, in order to recover more details, a wavelet ...
Zhengwei Shen
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Bulletin of the London Mathematical Society, Volume 54, Issue 2, Page 590-608, April 2022., 2022 Abstract We construct an example of a smooth convex function on the plane with a strict minimum at zero, which is real analytic except at zero, for which Thom's gradient conjecture fails both at zero and infinity. More precisely, the gradient orbits of the function spiral around zero and at infinity.
Aris Daniilidis +2 more
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Factorization of completely positive matrices using iterative projected gradient steps
Numerical Linear Algebra with Applications, Volume 28, Issue 6, December 2021., 2021 Abstract We aim to factorize a completely positive matrix by using an optimization approach which consists in the minimization of a nonconvex smooth function over a convex and compact set. To solve this problem we propose a projected gradient algorithm with parameters that take into account the effects of relaxation and inertia.
Radu Ioan Boţ, Dang‐Khoa Nguyen
wiley +1 more source
A LogTVSCAD Nonconvex Regularization Model for Image Deblurring in the Presence of Impulse Noise
Discrete Dynamics in Nature and Society, Volume 2021, Issue 1, 2021., 2021 This paper proposes a nonconvex model (called LogTVSCAD) for deblurring images with impulsive noises, using the log‐function penalty as the regularizer and adopting the smoothly clipped absolute deviation (SCAD) function as the data‐fitting term. The proposed nonconvex model can effectively overcome the poor performance of the classical TVL1 model for ...
Zhijun Luo +3 more
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Convergence Rate Analysis of the Proximal Difference of the Convex Algorithm
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 In this paper, we study the convergence rate of the proximal difference of the convex algorithm for the problem with a strong convex function and two convex functions. By making full use of the special structure of the difference of convex decomposition, we prove that the convergence rate of the proximal difference of the convex algorithm is linear ...
Xueyong Wang +4 more
wiley +1 more source
Polychromatic X-ray CT Image Reconstruction and Mass-Attenuation Spectrum Estimation [PDF]
, 2015 We develop a method for sparse image reconstruction from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident-energy spectrum are unknown.
Dogandžić, Aleksandar, Gu, Renliang
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Mathematical Problems in Engineering, Volume 2016, Issue 1, 2016., 2016 We deal with a class of problems whose objective functions are compositions of nonconvex nonsmooth functions, which has a wide range of applications in signal/image processing. We introduce a new auxiliary variable, and an efficient general proximal alternating minimization algorithm is proposed.
Xiaoya Zhang +3 more
wiley +1 more source
Best Pair Formulation & Accelerated Scheme for Non-convex Principal Component Pursuit
, 2019 The best pair problem aims to find a pair of points that minimize the distance between two disjoint sets. In this paper, we formulate the classical robust principal component analysis (RPCA) as the best pair; which was not considered before. We design an
Dutta, Aritra +3 more
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