scholarly journals Hybrid steepest-descent viscosity methods for triple hierarchical variational inequalities with constraints of mixed equilibria and bilevel variational inequalities

2017 ◽  
Vol 10 (03) ◽  
pp. 1126-1147
Author(s):  
Lu-Chuan Ceng ◽  
Yeong-Cheng Liou ◽  
Ching-Feng Wen ◽  
Abdul Latif
Keyword(s):  
Variational Inequalities ◽  
Steepest Descent ◽  
Triple Hierarchical Variational Inequalities ◽  
Mixed Equilibria ◽  
Hierarchical Variational Inequalities

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 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.

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