A general framework for ADMM acceleration

Buccini, Alessandro; Dell'Acqua, Pietro; Donatelli, Marco

doi:10.1007/s11075-019-00839-y

Cited by 22 publications

(12 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Matters of future research include the application of this method to real data and an efficient implementation exploiting Krylov subspaces. Moreover, we plan on using the Alternating Direction Multiplier Method (ADMM) and its accelerations (see, e.g., [4,6,19]) for efficiently computing a solution of (1.3).…”

Section: Discussionmentioning

confidence: 99%

A variational non-linear constrained model for the inversion of FDEM data

Buccini,

de Alba

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Reconstructing the structure of the soil using non invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of Frequency Domain Electromagnetic (FDEM) induction devices. Inverting FDEM data is a very challenging inverse problem, as the problem is extremely ill-posed, i.e., sensible to the presence of noise in the measured data, and non-linear. Regularization methods aim at reducing this sensitivity. In this paper we develop a regularization method to invert FDEM data. We propose to determine the electrical conductivity of the ground by solving a variational problem. The minimized functional is made up by the sum of two terms, the data fitting term ensures that the recovered solution fits the measured data, while the regularization term enforces sparsity on the Laplacian of the solution. The trade-off between the two terms is determined by the regularization parameter. This is achieved by minimizing an 2 − q functional with 0 < q ≤ 2. Since the functional we wish to minimize is nonconvex, we show that the variational problem admits a solution. Moreover, we prove that, if the regularization parameter is tuned accordingly to the amount of noise present in the data, this model induces a regularization method. Some selected numerical examples show the good performances of our proposal.

show abstract

Section: Discussionmentioning

confidence: 99%

A variational non-linear constrained model for the inversion of FDEM data

Buccini,

de Alba

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Rather we wish to show the potential of L ω as a regularization operator. Nevertheless, it is possible to accelerate the convergence of ADMM by extrapolation methods to improve the convergence rate of ADMM; see, e.g., [9,30]. We would like to stress that, in our experiments, the proposed algorithm converges in a reasonable number of iterations, and, while it could benefit from an acceleration, accelerating it is not essential for our purposes.…”

Section: Bianchi a Buccini M Donatelli And E Randazzomentioning

confidence: 94%

Graph Laplacian for image deblurring

Bianchi¹,

Buccini²,

Donatelli³

et al. 2021

etna

Self Cite

View full text Add to dashboard Cite

Image deblurring is a relevant problem in many fields of science and engineering. To solve this problem, many different approaches have been proposed, and, among the various methods, variational ones are extremely popular. These approaches substitute the original problem with a minimization problem where the functional is composed of two terms, a data fidelity term and a regularization term. In this paper we propose, in the classical non-negative constrained 2 -1 minimization framework, the use of the graph Laplacian as regularization operator. Firstly, we describe how to construct the graph Laplacian from the observed noisy and blurred image. Once the graph Laplacian has been built, we efficiently solve the proposed minimization problem by splitting the convolution operator and the graph Laplacian by the Alternating Direction Multiplier Method (ADMM). Some selected numerical examples show the good performances of the proposed algorithm.

show abstract

“…We use acc to denote an acceleration technique, which often corresponds to a linear combination. This general acceleration framework for ADMM and its variants has been documented in [134], however the theoretical convergence rate characterizations for such general acceleration framework remain to be addressed. This represents another important and significant future research direction.…”

Section: B Admm Accelerationmentioning

confidence: 99%

A Survey of ADMM Variants for Distributed Optimization: Problems, Algorithms and Features

Yu¹,

Guan²,

Jia³

et al. 2022

Preprint

View full text Add to dashboard Cite

By coordinating terminal smart devices or microprocessors to engage in cooperative computation to achieve systemlevel targets, distributed optimization is incrementally favored by both engineering and computer science. The well-known alternating direction method of multipliers (ADMM) has turned out to be one of the most popular tools for distributed optimization due to many advantages, such as modular structure, superior convergence, easy implementation and high flexibility. In the past decade, ADMM has experienced widespread developments. The developments manifest in both handling more general problems and enabling more effective implementation. Specifically, the method has been generalized to broad classes of problems (i.e., multi-block, coupled objective, nonconvex, etc.). Besides, it has been extensively reinforced for more effective implementation, such as improved convergence rate, easier subproblems, higher computation efficiency, flexible communication, compatible with inaccurate information, robust to communication delays, etc. These developments lead to a plentiful of ADMM variants to be celebrated by broad areas ranging from smart grids, smart buildings, wireless communications, machine learning and beyond. However, there lacks a survey to document those developments and discern the results. To achieve such a goal, this paper provides a comprehensive survey on ADMM variants. Particularly, we discern the five major classes of problems that have been mostly concerned and discuss the related ADMM variants in terms of main ideas, main assumptions, convergence behaviors and main features. In addition, we figure out several important future research directions to be addressed. This survey is expected to work as a tutorial for both developing distributed optimization in broad areas and identifying existing research gaps.

show abstract

A general framework for ADMM acceleration

Cited by 22 publications

References 23 publications

A variational non-linear constrained model for the inversion of FDEM data

A variational non-linear constrained model for the inversion of FDEM data

Graph Laplacian for image deblurring

A Survey of ADMM Variants for Distributed Optimization: Problems, Algorithms and Features

Contact Info

Product

Resources

About