Accelerated hybrid viscosity and steepest-descent method for proximal split feasibility problems

Optimization ◽  
2017 ◽  
Vol 67 (4) ◽  
pp. 475-492 ◽  
Author(s):  
Yekini Shehu ◽  
Olaniyi. S. Iyiola
Keyword(s):  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Split Feasibility Problems ◽  
Proximal Split Feasibility Problems ◽  
Split Feasibility

scholarly journals Convergence Theorems for the Variational Inequality Problems and Split Feasibility Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Panisa Lohawech ◽  
Anchalee Kaewcharoen ◽  
Ali Farajzadeh
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Descent Method ◽  
Variational Inequality Problems ◽  
Steepest Descent Method ◽  
Split Feasibility Problems ◽  
The Common ◽  
Split Feasibility

In this paper, we establish an iterative algorithm by combining Yamada’s hybrid steepest descent method and Wang’s algorithm for finding the common solutions of variational inequality problems and split feasibility problems. The strong convergence of the sequence generated by our suggested iterative algorithm to such a common solution is proved in the setting of Hilbert spaces under some suitable assumptions imposed on the parameters. Moreover, we propose iterative algorithms for finding the common solutions of variational inequality problems and multiple-sets split feasibility problems. Finally, we also give numerical examples for illustrating our algorithms.

scholarly journals A Learning Method for Neural Networks Based on a Pseudoinverse Technique

1996 ◽  
Vol 3 (3) ◽  
pp. 201-209 ◽  
Author(s):  
Chinmoy Pal ◽  
Ichiro Hagiwara ◽  
Naoki Kayaba ◽  
Shin Morishita
Keyword(s):  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Learning Method ◽  
Theoretical Formulation ◽  
Learning Capability ◽  
Fast Learning ◽  
Backpropagation Method ◽  
Mass Spring ◽  
Exclusive Or

A theoretical formulation of a fast learning method based on a pseudoinverse technique is presented. The efficiency and robustness of the method are verified with the help of an Exclusive OR problem and a dynamic system identification of a linear single degree of freedom mass–spring problem. It is observed that, compared with the conventional backpropagation method, the proposed method has a better convergence rate and a higher degree of learning accuracy with a lower equivalent learning coefficient. It is also found that unlike the steepest descent method, the learning capability of which is dependent on the value of the learning coefficient ν, the proposed pseudoinverse based backpropagation algorithm is comparatively robust with respect to its equivalent variable learning coefficient. A combination of the pseudoinverse method and the steepest descent method is proposed for a faster, more accurate learning capability.

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