scholarly journals MADAM: a parallel exact solver for max-cut based on semidefinite programming and ADMM

2021 ◽  
Vol 80 (2) ◽  
pp. 347-375
Author(s):  
Timotej Hrga ◽  
Janez Povh
Keyword(s):  
State Of The Art ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
Dual Variable ◽  
Maximum Weight ◽  
New Approach ◽  
Parallel Solver ◽  
Alternating Direction ◽  
Computationally Expensive ◽  
Serial Algorithm

AbstractWe present , a parallel semidefinite-based exact solver for Max-Cut, a problem of finding the cut with the maximum weight in a given graph. The algorithm uses the branch and bound paradigm that applies the alternating direction method of multipliers as the bounding routine to solve the basic semidefinite relaxation strengthened by a subset of hypermetric inequalities. The benefit of the new approach is a less computationally expensive update rule for the dual variable with respect to the inequality constraints. We provide a theoretical convergence of the algorithm as well as extensive computational experiments with this method, to show that our algorithm outperforms state-of-the-art approaches. Furthermore, by combining algorithmic ingredients from the serial algorithm, we develop an efficient distributed parallel solver based on MPI.

scholarly journals Two Efficient Algorithms for Orthogonal Nonnegative Matrix Factorization

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jing Wu ◽  
Bin Chen ◽  
Tao Han
Keyword(s):  
Gene Expression ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
State Of The Art ◽  
Nonnegative Matrix ◽  
Alternating Direction Method ◽  
Data Matrix ◽  
Popular Method ◽  
Alternating Direction ◽  
Expression Classification

Nonnegative matrix factorization (NMF) is a popular method for the multivariate analysis of nonnegative data. It involves decomposing a data matrix into a product of two factor matrices with all entries restricted to being nonnegative. Orthogonal nonnegative matrix factorization (ONMF) has been introduced recently. This method has demonstrated remarkable performance in clustering tasks, such as gene expression classification. In this study, we introduce two convergence methods for solving ONMF. First, we design a convergent orthogonal algorithm based on the Lagrange multiplier method. Second, we propose an approach that is based on the alternating direction method. Finally, we demonstrate that the two proposed approaches tend to deliver higher-quality solutions and perform better in clustering tasks compared with a state-of-the-art ONMF.

scholarly journals Efficient Proximal Gradient Algorithms for Joint Graphical Lasso

Entropy ◽  
2021 ◽  
Vol 23 (12) ◽  
pp. 1623
Author(s):  
Jie Chen ◽  
Ryosuke Shimmura ◽  
Joe Suzuki
Keyword(s):  
Graphical Model ◽  
State Of The Art ◽  
High Accuracy ◽  
Alternating Direction Method ◽  
Main Approach ◽  
First Order ◽  
Gradient Algorithms ◽  
Graphical Lasso ◽  
Alternating Direction ◽  
Accuracy And Precision

We consider learning as an undirected graphical model from sparse data. While several efficient algorithms have been proposed for graphical lasso (GL), the alternating direction method of multipliers (ADMM) is the main approach taken concerning joint graphical lasso (JGL). We propose proximal gradient procedures with and without a backtracking option for the JGL. These procedures are first-order methods and relatively simple, and the subproblems are solved efficiently in closed form. We further show the boundedness for the solution of the JGL problem and the iterates in the algorithms. The numerical results indicate that the proposed algorithms can achieve high accuracy and precision, and their efficiency is competitive with state-of-the-art algorithms.

scholarly journals Fusing Multiple Multiband Images

2018 ◽  
Vol 4 (10) ◽  
pp. 118 ◽  
Author(s):  
Reza Arablouei
Keyword(s):  
State Of The Art ◽  
Likelihood Estimation ◽  
Alternating Direction Method ◽  
Natural Images ◽  
Hyperspectral Images ◽  
Superior Performance ◽  
Method Of Multipliers ◽  
Alternating Direction ◽  
Abrupt Changes ◽  
Fused Image

High-resolution hyperspectral images are in great demand but hard to acquire due to several existing fundamental and technical limitations. A practical way around this is to fuse multiple multiband images of the same scene with complementary spatial and spectral resolutions. We propose an algorithm for fusing an arbitrary number of coregistered multiband, i.e., panchromatic, multispectral, or hyperspectral, images through estimating the endmember and their abundances in the fused image. To this end, we use the forward observation and linear mixture models and formulate an appropriate maximum-likelihood estimation problem. Then, we regularize the problem via a vector total-variation penalty and the non-negativity/sum-to-one constraints on the endmember abundances and solve it using the alternating direction method of multipliers. The regularization facilitates exploiting the prior knowledge that natural images are mostly composed of piecewise smooth regions with limited abrupt changes, i.e., edges, as well as coping with potential ill-posedness of the fusion problem. Experiments with multiband images constructed from real-world hyperspectral images reveal the superior performance of the proposed algorithm in comparison with the state-of-the-art algorithms, which need to be used in tandem to fuse more than two multiband images.

scholarly journals An Alternating Direction Method for Mixed Gaussian Plus Impulse Noise Removal

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Si Wang ◽  
Ting-Zhu Huang ◽  
Xi-le Zhao ◽  
Jun Liu
Keyword(s):  
Total Variation ◽  
Numerical Experiments ◽  
Impulse Noise ◽  
State Of The Art ◽  
Noise Removal ◽  
Alternating Direction Method ◽  
Impulse Noise Removal ◽  
Alternating Direction ◽  
Total Variation Model ◽  
Blurred Images

A combined total variation and high-order total variation model is proposed to restore blurred images corrupted by impulse noise or mixed Gaussian plus impulse noise. We attack the proposed scheme with an alternating direction method of multipliers (ADMM). Numerical experiments demonstrate the efficiency of the proposed method and the performance of the proposed method is competitive with the existing state-of-the-art methods.

Alternating Direction Method of Solving Nonlinear Programming with Inequality Constrained

2014 ◽  
Vol 651-653 ◽  
pp. 2107-2111
Author(s):  
Ai Fen Feng ◽  
Li Ming Zhang ◽  
Zhen Xia Xue
Keyword(s):  
Nonlinear Programming ◽  
Lagrange Function ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
New Class ◽  
Ncp Function ◽  
Kkt Point ◽  
Alternating Direction ◽  
Local Point ◽  
Unconstrained Problem

This paper, a new class of augmented Lagrange functions with the new NCP function is proposed for the minimization of a smooth function subject to inequality constraints. Under some conditions, we prove of the equivalences of the KKT point and local point and globe point between primal constrained nonlinear programming problem and the new unconstrained problem. By the character of augmented Lagrange function, the algorithm which uses alternating direction method is constructed and proved convergence.

The Engineering Application of Improved Alternating Direction Method for Solving Power Systems Multi-Area Dispatch Problem

2015 ◽  
Vol 740 ◽  
pp. 929-932
Author(s):  
Ya Ming Ren ◽  
Shu Min Fei ◽  
Hai Kun Wei
Keyword(s):  
Power Systems ◽  
Economic Dispatch ◽  
Engineering Application ◽  
Inequality Constraints ◽  
Alternating Direction Method ◽  
Penalty Parameter ◽  
Alternating Direction ◽  
Equality And Inequality Constraints ◽  
Convergence Performance ◽  
Consistency Constraint

The alternating direction method has been widespread used to solve multi-area economic dispatch problem. Compared with traditional centered economic dispatch, alternating direction method divides centered optimal problem into completely independent sub-problems while the corresponding equality and inequality constraints are satisfied. However, plenty of applications show that the choice of penalty parameter for the consistency constraint has an important influence on the convergence performance of alternating direction method. In this paper, we proposed a novel improved alternating direction method. To be more exact, the key is to adjust penalty parameter based on iterative information of alternating direction method. Numerical results illustrate the proposed method has better stability in convergence.

scholarly journals Economic Genome Assembly from Low Coverage Illumina and Nanopore Data

2020 ◽  
Author(s):  
Thomas Gatter ◽  
Sarah von Löhneysen ◽  
Polina Drozdova ◽  
Tom Hartmann ◽  
Peter F. Stadler
Keyword(s):  
Genomic Sequence ◽  
State Of The Art ◽  
Fruit Fly ◽  
Computational Effort ◽  
Maximum Weight ◽  
New Approach ◽  
Short Read ◽  
Long Reads ◽  
Long Read ◽  
Low Coverage

AbstractWe describe a new approach to assemble genomes from a combination of low-coverage short and long reads. LazyBastard starts from a bipartite overlap graph between long reads and restrictively filtered short-read unitigs, which are then reduced to a long-read overlap graph G. Edges are removed from G to obtain first a consistent orientation and then a DAG. Using heuristics based on properties of proper interval graphs, contigs are extracted as maximum weight paths. These are translated into genomic sequence only in the final step. A prototype implementation of LazyBastard, entirely written in python, not only yields significantly more accurate assemblies of the yeast and fruit fly genomes compared to state-of-the-art pipelines but also requires much less computational effort.FundingRSF / Helmholtz Association 18-44-06201; Deutsche Academische Austauschdienst, DFG STA 850/19-2 within SPP 1738; German Federal Ministery of Education an Research 031A538A, de.NBI-RBC

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