scholarly journals Random permutations fix a worst case for cyclic coordinate descent

2018 ◽  
Vol 39 (3) ◽  
pp. 1246-1275 ◽  
Author(s):  
Ching-pei Lee ◽  
Stephen J Wright
Keyword(s):  
Nonlinear Function ◽  
Quadratic Function ◽  
Random Permutation ◽  
Coordinate Descent ◽  
Random Permutations ◽  
Worst Case ◽  
Computational Performance ◽  
Technical Report ◽  
Cyclic Coordinate Descent ◽  
Better Than

Abstract Variants of the coordinate descent approach for minimizing a nonlinear function are distinguished in part by the order in which coordinates are considered for relaxation. Three common orderings are cyclic (CCD), in which we cycle through the components of $x$ in order; randomized (RCD), in which the component to update is selected randomly and independently at each iteration; and random-permutations cyclic (RPCD), which differs from CCD only in that a random permutation is applied to the variables at the start of each cycle. Known convergence guarantees are weaker for CCD and RPCD than for RCD, though in most practical cases, computational performance is similar among all these variants. There is a certain type of quadratic function for which CCD is significantly slower than for RCD; a recent paper by Sun & Ye (2016, Worst-case complexity of cyclic coordinate descent: $O(n^2)$ gap with randomized version. Technical Report. Stanford, CA: Department of Management Science and Engineering, Stanford University. arXiv:1604.07130) has explored the poor behavior of CCD on functions of this type. The RPCD approach performs well on these functions, even better than RCD in a certain regime. This paper explains the good behavior of RPCD with a tight analysis.

scholarly journals Analyzing random permutations for cyclic coordinate descent

2020 ◽  
Vol 89 (325) ◽  
pp. 2217-2248 ◽  
Author(s):  
Stephen J. Wright ◽  
Ching-pei Lee
Keyword(s):  
Coordinate Descent ◽  
Random Permutations ◽  
Cyclic Coordinate Descent

scholarly journals Managing contamination delay to improve Timing Speculation architectures

2016 ◽  
Vol 2 ◽  
pp. e79 ◽  
Author(s):  
Naga Durga Prasad Avirneni ◽  
Prem Kumar Ramesh ◽  
Arun K. Somani
Keyword(s):  
Performance Improvement ◽  
Short Path ◽  
Performance Enhancement ◽  
Propagation Delay ◽  
Performance Impact ◽  
Worst Case ◽  
Circuit Delay ◽  
Timing Speculation ◽  
Better Than

Timing Speculation (TS) is a widely known method for realizing better-than-worst-case systems. Aggressive clocking, realizable by TS, enable systems to operate beyond specified safe frequency limits to effectively exploit the data dependent circuit delay. However, the range of aggressive clocking for performance enhancement under TS is restricted by short paths. In this paper, we show that increasing the lengths of short paths of the circuit increases the effectiveness of TS, leading to performance improvement. Also, we propose an algorithm to efficiently add delay buffers to selected short paths while keeping down the area penalty. We present our algorithm results for ISCAS-85 suite and show that it is possible to increase the circuit contamination delay by up to 30% without affecting the propagation delay. We also explore the possibility of increasing short path delays further by relaxing the constraint on propagation delay and analyze the performance impact.

Generation of the symmetric group Sn2

2021 ◽  
pp. 2150107
Author(s):  
Carlos Zequeira Sánchez ◽  
Evaristo José Madarro Capó ◽  
Guillermo Sosa-Gómez
Keyword(s):  
Symmetric Group ◽  
Random Element ◽  
Matrix Representation ◽  
Random Permutation ◽  
Random Permutations ◽  
Dimension Formula ◽  
Indispensable Tool

In various scenarios today, the generation of random permutations has become an indispensable tool. Since random permutation of dimension [Formula: see text] is a random element of the symmetric group [Formula: see text], it is necessary to have algorithms capable of generating any permutation. This work demonstrates that it is possible to generate the symmetric group [Formula: see text] by shifting the components of a particular matrix representation of each permutation.

scholarly journals Hybrid ARIMA and Neural Network Modelling Applied to Telecommunications in Urban Environments in the Amazon Region

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ramz L. Fraiha Lopes ◽  
Simone G. C. Fraiha ◽  
Vinicius D. Lima ◽  
Herminio S. Gomes ◽  
Gervásio P. S. Cavalcante
Keyword(s):  
Neural Network ◽  
Moving Average ◽  
Urban Environments ◽  
Digital Television ◽  
Network Modelling ◽  
Worst Case ◽  
Autoregressive Integrated Moving Average ◽  
Neural Network Modelling ◽  
Better Than

This study explores the use of a hybrid Autoregressive Integrated Moving Average (ARIMA) and Neural Network modelling for estimates of the electric field along vertical paths (buildings) close to Digital Television (DTV) transmitters. The work was carried out in Belém city, one of the most urbanized cities in the Brazilian Amazon and includes a case study of the application of this modelling within the subscenarios found in Belém. Its results were compared with the ITU recommendations P. 1546-5 and proved to be better in every subscenario analysed. In the worst case, the estimate of the model was approximately 65% better than that of the ITU. We also compared this modelling with a classic modelling technique: the Least Squares (LS) method. In most situations, the hybrid model achieved better results than the LS.

SPE Publishes Technical Report on Worst-Case Discharges

2015 ◽  
Vol 67 (06) ◽  
pp. 74-74
Author(s):  
_ JPT staff
Keyword(s):  
Worst Case ◽  
Technical Report

scholarly journals Dictionary Learning Based on Nonnegative Matrix Factorization Using Parallel Coordinate Descent

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zunyi Tang ◽  
Shuxue Ding ◽  
Zhenni Li ◽  
Linlin Jiang
Keyword(s):  
Sparse Representation ◽  
Dictionary Learning ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Coordinate Descent ◽  
Multispectral Data ◽  
Overcomplete Dictionary ◽  
Novel Method ◽  
Better Than

Sparse representation of signals via an overcomplete dictionary has recently received much attention as it has produced promising results in various applications. Since the nonnegativities of the signals and the dictionary are required in some applications, for example, multispectral data analysis, the conventional dictionary learning methods imposed simply with nonnegativity may become inapplicable. In this paper, we propose a novel method for learning a nonnegative, overcomplete dictionary for such a case. This is accomplished by posing the sparse representation of nonnegative signals as a problem of nonnegative matrix factorization (NMF) with a sparsity constraint. By employing the coordinate descent strategy for optimization and extending it to multivariable case for processing in parallel, we develop a so-called parallel coordinate descent dictionary learning (PCDDL) algorithm, which is structured by iteratively solving the two optimal problems, the learning process of the dictionary and the estimating process of the coefficients for constructing the signals. Numerical experiments demonstrate that the proposed algorithm performs better than the conventional nonnegative K-SVD (NN-KSVD) algorithm and several other algorithms for comparison. What is more, its computational consumption is remarkably lower than that of the compared algorithms.

scholarly journals On the Efficiency of Random Permutation for ADMM and Coordinate Descent

2020 ◽  
Vol 45 (1) ◽  
pp. 233-271 ◽  
Author(s):  
Ruoyu Sun ◽  
Zhi-Quan Luo ◽  
Yinyu Ye
Keyword(s):  
Random Permutation ◽  
Coordinate Descent

scholarly journals A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

2019 ◽  
Vol 9 (24) ◽  
pp. 5461
Author(s):  
Yuhan Chen ◽  
Xiao Luo ◽  
Baoling Han ◽  
Yan Jia ◽  
Guanhao Liang ◽  
...  
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Inverse Kinematics ◽  
Optimization Problem ◽  
Robot Manipulators ◽  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method ◽  
Prismatic Joints ◽  
Cyclic Coordinate Descent

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.

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