Using the coordinate descent method in variance-mesh systems in solving problems of elasticity theory

1985 ◽  
Vol 17 (9) ◽  
pp. 1310-1316
Author(s):  
N. V. Vasilenko ◽  
A. E. Babenko ◽  
A. Yu. Chirkov
Keyword(s):  
Elasticity Theory ◽  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method

Coordinate Descent Method for k-means

2021 ◽  
pp. 1-1
Author(s):  
Feiping Nie ◽  
Jingjing Xue ◽  
Danyang Wu ◽  
Rong Wang ◽  
Hui Li ◽  
...  
Keyword(s):  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method

scholarly journals A Randomized Coordinate Descent Method with Volume Sampling

2020 ◽  
Vol 30 (3) ◽  
pp. 1878-1904
Author(s):  
Anton Rodomanov ◽  
Dmitry Kropotov
Keyword(s):  
Descent Method ◽  
Coordinate Descent ◽  
Coordinate Descent Method

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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