Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems

Sun, Tao; Jiang, Hao; Cheng, Lizhi; Zhu, Wei

doi:10.1109/tsp.2018.2868269

Cited by 34 publications

(17 citation statements)

References 47 publications

(76 reference statements)

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“…However, according to the definition of q,ε -norm (2), problem (5) is nonconvex and the traditional ADMM algorithm can not solve this problem effectively. In paper [10], the reweighted ADMM is proposed to solve a similar problem. We employ the same techniques proposed in [10].…”

Section: The Nonconvex Algorithmmentioning

confidence: 99%

A Nonconvex Implementation of Sparse Subspace Clustering: Algorithm and Convergence Analysis

Deng

Sun

et al. 2020

IEEE Access

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Subspace clustering has been widely applied to detect meaningful clusters in high-dimensional data spaces. And the sparse subspace clustering (SSC) obtains superior clustering performance by solving a relaxed 0-minimization problem with 1-norm. Although the use of 1-norm instead of the 0 one can make the object function convex, it causes large errors on large coefficients in some cases. In this paper, we study the sparse subspace clustering algorithm based on a nonconvex modeling formulation. Specifically, we introduce a nonconvex pseudo-norm that makes a better approximation to the 0-minimization than the traditional 1-minimization framework and consequently finds a better affinity matrix. However, this formulation makes the optimization task challenging due to that the traditional alternating direction method of multipliers (ADMM) encounters troubles in solving the nonconvex subproblems. In view of this, the reweighted techniques are employed in making these subproblems convex and easily solvable. We provide several guarantees to derive the convergence results, which proves that the nonconvex algorithm is globally convergent to a critical point. Experiments on two real-world problems of motion segmentation and face clustering show that our method outperforms state-of-the-art techniques. INDEX TERMS Sparse subspace clustering, nonconvex approximation, ADMM, reweighted algorithms.

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Section: The Nonconvex Algorithmmentioning

confidence: 99%

A Nonconvex Implementation of Sparse Subspace Clustering: Algorithm and Convergence Analysis

Deng

Sun

et al. 2020

IEEE Access

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“…Therefore, problems (4), (10) and (12) are non-convex and it is difficult to obtain the global optimum. In what follows, we design heuristic optimization algorithms to solve the problems locally via the penalty dual decomposition (PDD) method and the successive convex approximation (SCA) methods [30]- [33].…”

Section: Design Of Optimization Algorithmsmentioning

confidence: 99%

“…dual ascent method) and in particular achieves convergence without the need of specific assumptions for the objective function, i.e. strict convexity and finiteness [30]- [33]. The smaller the value of ρ, the greater the probability of equality (33d) holds.…”

Section: B Convexity Of Problemmentioning

confidence: 99%

Cloud-Edge Coordinated Processing: Low-Latency Multicasting Transmission

Ren

Wang

et al. 2019

IEEE J. Select. Areas Commun.

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Recently, edge caching and multicasting arise as two promising technologies to support highdata-rate and low-latency delivery in wireless communication networks. In this paper, we design three transmission schemes aiming to minimize the delivery latency for cache-enabled multigroup multicasting networks. In particular, full caching bulk transmission scheme is first designed as a performance benchmark for the ideal situation where the caching capability of each enhanced remote radio head (eRRH) is sufficient large to cache all files. For the practical situation where the caching capability of each eRRH is limited, we further design two transmission schemes, namely partial caching bulk transmission (PCBT) and partial caching pipelined transmission (PCPT) schemes. In the PCBT scheme, eRRHs first fetch the uncached requested files from the baseband unit (BBU) and then all requested files are simultaneously transmitted to the users. In the PCPT scheme, eRRHs first transmit the cached requested files while fetching the uncached requested files from the BBU. Then, the remaining cached requested files and fetched uncached requested files are simultaneously transmitted to the users. The design goal of the three transmission schemes is to minimize the delivery latency, subject to some practical constraints. Efficient algorithms are developed for the low-latency cloud-edge coordinated transmission strategies. Numerical results are provided to evaluate the performance of the proposed ). 2 transmission schemes and show that the PCPT scheme outperforms the PCBT scheme in terms of the delivery latency criterion. Index TermsCache-enabled radio access networks, delivery latency, multigroup multicasting, non-convex optimization. I. INTRODUCTIONDriven by the visions of ultra-high-definition video, intelligent driving, and Internet of Things, high-data-rate and low-latency delivery become two key performance indicators of future wireless communication networks [1]. The vast resources available in the cloud radio access server can be leveraged to deliver elastic computing power and storage to support resource-constrained enduser devices [2]. However, it is not suitable for a large set of cloud-based applications such as the delay-sensitive ones, since end devices in general are far away from the central cloud server, i.e., data center [3], [4]. To overcome these drawbacks, caching popular content at the network edge during the off-peak period is proved to be a powerful technique to realize low-latency delivery for some specific applications, such as real-time online gaming, virtual reality, and ultra-highdefinition video streaming, in next-generation communication systems [5]- [7]. Consequently, an evolved network architecture, labeled as cache-enabled radio access networks (RANs), has emerged to satisfy the demands of ultra-low-latency delivery by migrating the computing and caching functions from the cloud to the network edge [7]- [9]. In the cache-enabled RANs, the cache-enabled radio access nodes named as enhanced remote radio he...

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“…The Lena image is used in the numerical experiments. We solve (3) when q = 0.5, and use the nonconvex ADMM proposed in [9] for comparison. The performance of the proposed deblurring algorithms is routinely measured by means of the signal-to-noise ratio (SNR)…”

Section: Application To Image Deblurringmentioning

confidence: 99%

Iteratively Reweighted Penalty Alternating Minimization Methods with Continuation for Image Deblurring

Sun

Jiang

et al. 2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating minimization algorithm. To speed up the algorithm, we also apply the continuation strategy to the penalty parameter. A convergence result is proved for the algorithm. Compared with the nonconvex ADMM, the proposed algorithm enjoys both theoretical and computational advantages like weaker convergence requirements and faster speed. Numerical results demonstrate the efficiency of the proposed algorithm.

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Iteratively Linearized Reweighted Alternating Direction Method of Multipliers for a Class of Nonconvex Problems

Cited by 34 publications

References 47 publications

A Nonconvex Implementation of Sparse Subspace Clustering: Algorithm and Convergence Analysis

A Nonconvex Implementation of Sparse Subspace Clustering: Algorithm and Convergence Analysis

Cloud-Edge Coordinated Processing: Low-Latency Multicasting Transmission

Iteratively Reweighted Penalty Alternating Minimization Methods with Continuation for Image Deblurring

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