scholarly journals Composite steepest-descent method for the triple hierarchical variational inequalities

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4403-4419
Author(s):  
Lu-Chuan Ceng ◽  
Jen-Chih Yao ◽  
Yonghong Yao
Keyword(s):  
Variational Inequality Problem ◽  
Real Hilbert Space ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Mild Conditions ◽  
Triple Hierarchical Variational Inequalities ◽  
Steepest Descent Algorithm ◽  
Triple Hierarchical Variational Inequality ◽  
Hierarchical Variational Inequalities

In this paper, we introduce and analyze a composite steepest-descent algorithm for solving the triple hierarchical variational inequality problem in a real Hilbert space. Under mild conditions, the strong convergence of the iteration sequences generated by the algorithm is established.

scholarly journals Hybrid Steepest Descent Viscosity Method for Triple Hierarchical Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
L.-C. Ceng ◽  
Q. H. Ansari ◽  
C.-F. Wen
Keyword(s):  
Approximate Solution ◽  
Variational Inequality Problem ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Viscosity Method ◽  
Hybrid Steepest Descent Method ◽  
Triple Hierarchical Variational Inequalities ◽  
Triple Hierarchical Variational Inequality ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (in short, THVIP). By combining hybrid steepest descent method, viscosity method, and projection method, we propose an approximation method to compute the approximate solution of THVIP. We also study the strong convergence of the sequences generated by the proposed method to a solution of THVIP.

scholarly journals Steepest-Descent Approach to Triple Hierarchical Constrained Optimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-19
Author(s):  
Lu-Chuan Ceng ◽  
Cheng-Wen Liao ◽  
Chin-Tzong Pang ◽  
Ching-Feng Wen
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Projection Algorithm ◽  
Fixed Point Set

We introduce and analyze a hybrid steepest-descent algorithm by combining Korpelevich’s extragradient method, the steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to the unique solution of a triple hierarchical constrained optimization problem (THCOP) over the common fixed point set of finitely many nonexpansive mappings, with constraints of finitely many generalized mixed equilibrium problems (GMEPs), finitely many variational inclusions, and a convex minimization problem (CMP) in a real Hilbert space.

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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