An Accelerated Linearized Alternating Direction Method of Multipliers

Ouyang, Yijian; Chen, Yunmei; Lan, Guanghui; Pasiliao, Eduardo L.

doi:10.21236/ada595588

Cited by 99 publications

(275 citation statements)

References 45 publications

Supporting

Mentioning

258

Contrasting

Unclassified

Order By: Relevance

“…The early iteration speed of BARISTA is due to its tight approximation of the Hessian of the cost function via the diagonal majorizers developed in this paper and the use of Nesterov momentum acceleration. Nesterov momentum has been added to AL algorithms in some cases [22], although those algorithms require an estimate of the Lipschitz constant, so the diagonal majorizers presented here may be useful for those methods.…”

Section: Discussionmentioning

confidence: 99%

Fast Parallel MR Image Reconstruction via B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithms (BARISTA)

Muckley

Noll

Fessler

2015

IEEE Trans. Med. Imaging

View full text Add to dashboard Cite

Sparsity-promoting regularization is useful for combining compressed sensing assumptions with parallel MRI for reducing scan time while preserving image quality. Variable splitting algorithms are the current state-of-the-art algorithms for SENSE-type MR image reconstruction with sparsity-promoting regularization. These methods are very general and have been observed to work with almost any regularizer; however, the tuning of associated convergence parameters is a commonly-cited hindrance in their adoption. Conversely, majorize-minimize algorithms based on a single Lipschitz constant have been observed to be slow in shift-variant applications such as SENSE-type MR image reconstruction since the associated Lipschitz constants are loose bounds for the shift-variant behavior. This paper bridges the gap between the Lipschitz constant and the shift-variant aspects of SENSE-type MR imaging by introducing majorizing matrices in the range of the regularizer matrix. The proposed majorize-minimize methods (called BARISTA) converge faster than state-of-the-art variable splitting algorithms when combined with momentum acceleration and adaptive momentum restarting. Furthermore, the tuning parameters associated with the proposed methods are unitless convergence tolerances that are easier to choose than the constraint penalty parameters required by variable splitting algorithms.

show abstract

Section: Discussionmentioning

confidence: 99%

Fast Parallel MR Image Reconstruction via B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithms (BARISTA)

Muckley

Noll

Fessler

2015

IEEE Trans. Med. Imaging

View full text Add to dashboard Cite

show abstract

“…Deterministic ADMM [163] Distributed computation Fast convergence Many samples needed per iteration to deal with stochasticity Stochastic ADMM [159], [160], [186] Stochastic and distributed computation…”

Section: Seldom Achieving Global Optimummentioning

confidence: 99%

Modeling and Analysis of Energy Harvesting and Smart Grid-Powered Wireless Communication Networks: A Contemporary Survey

Chen

et al. 2020

IEEE Trans. on Green Commun. Netw.

View full text Add to dashboard Cite

The advancements in smart power grid and the advocation of "green communications" have inspired the wireless communication networks to harness energy from ambient environments and operate in an energy-efficient manner for economic and ecological benefits. This article presents a contemporary review of recent breakthroughs on the utilization, redistribution, trading and planning of energy harvested in future wireless networks interoperating with smart grids. This article starts with classical models of renewable energy harvesting technologies. We embark on constrained operation and optimization of different energy harvesting wireless systems, such as point-to-point, multipoint-to-point, multipoint-to-multipoint, multi-hop, and multi-cell systems. We also review wireless power and information transfer technologies which provide a special implementation of energy harvesting wireless communications. A significant part of the article is devoted to the redistribution of redundant (unused) energy harvested within cellular networks, the energy planning under dynamic pricing when smart grids are in place, and two-way energy trading between cellular networks and smart grids. Applications of different optimization tools, such as convex optimization, Lagrangian dual-based method, subgradient method, and Lyapunov-based online optimization, are compared. This article also collates the potential applications of energy harvesting techniques in emerging (or upcoming) 5G/B5G communication systems. It is revealed that an effective redistribution and two-way trading of energy can significantly reduce the electricity bills of wireless service providers and decrease the consumption of brown energy. A list of interesting research directions are provided, requiring further investigation.Index Terms-5G/B5G communication networks, energy har-). The first two authors contributed equally to this work. vesting, smart grid, energy redistribution and trading, optimization techniques. arXiv:1912.13203v1 [eess.SY] 31 Dec 2019 EH and smart gridpowered wireless networks Types and models for RES (Sec. II) Smart grid-powered wireless networks (Sec. VIII) Wireless power and information transfer (Sec. VII) 5G/B5G applications of EH and smart gridpowered wireless networks (Sec. XI) Energy redistribution Energy planning under dynamic pricing (Sec. IX) Two-way energy trading and cooperation (Sec. X) EH-based wireless networks Point-to-point link (Sec. III) Multipoint-to-point system (Sec. IV) Multipoint-to-multipoint system (Sec. V) Multi-hop link (Sec. VI) Lessons learnt and future directions (Sec. XII) Fig. 1. The main structure of this article. from the aspects of network deployment, energy/spectrum efficiency, and delay/bandwidth versus power. Featuring energyharvesting wireless networks, beamforming techniques are reviewed in [22]. Energy scheduling, optimization, and application are presented in [23]. Circuit design, hardware implementation, EH techniques, and communication protocols are reviewed in [24]-[27] with specific emphases on radio frequen...

show abstract

“…Instead, we use “preconditioned” ADMM (PADMM) [61], [62] accelerated 1 using Nesterov momentum [64], essentially using a single FISTA step as the x -update in (12):

x^{i} \leftarrow soft false(z^{i - 1} - 1 \frac{1}{c} A^{'} false(bold-italicA z^{i - 1} - u^{i - 1} + b^{i - 1} false); 1 \frac{β}{μ c} false) .

t^{i} \leftarrow false(1 + \sqrt{1 + 4 {false(t^{i - 1} false)}^{2}} false) / 2.

z^{i} \leftarrow x^{i} + 1 \frac{t^{i - 1} - 1}{t^{i}} false(x^{i} - x^{i - 1} false) .

…”

Section: Solving the Majorized Objective With Admmmentioning

confidence: 99%

Undersampled Phase Retrieval With Outliers

Weller

Pnueli

Divon

et al. 2015

IEEE Trans. Comput. Imaging

View full text Add to dashboard Cite

This paper proposes a general framework for reconstructing sparse images from undersampled (squared)-magnitude data corrupted with outliers and noise. This phase retrieval method uses a layered approach, combining repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization of that majorizer using a preconditioned variant of the alternating direction method of multipliers (ADMM). Since phase retrieval is nonconvex, this implementation uses multiple initial majorization vectors. The introduction of a robust 1-norm data fit term that is better adapted to outliers exploits the generality of this framework. The derivation also describes a normalization scheme for the regularization parameter and a known adaptive heuristic for the ADMM penalty parameter. Both 1D Monte Carlo tests and 2D image reconstruction simulations suggest the proposed framework, with the robust data fit term, reduces the reconstruction error for data corrupted with both outliers and additive noise, relative to competing algorithms having the same total computation.

show abstract

An Accelerated Linearized Alternating Direction Method of Multipliers

Cited by 99 publications

References 45 publications

Fast Parallel MR Image Reconstruction via B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithms (BARISTA)

Fast Parallel MR Image Reconstruction via B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithms (BARISTA)

Modeling and Analysis of Energy Harvesting and Smart Grid-Powered Wireless Communication Networks: A Contemporary Survey

Undersampled Phase Retrieval With Outliers

Contact Info

Product

Resources

About