scholarly journals Fejér-monotone hybrid steepest descent method for affinely constrained and composite convex minimization tasks

Optimization ◽  
2018 ◽  
Vol 67 (11) ◽  
pp. 1963-2001 ◽  
Author(s):  
Konstantinos Slavakis ◽  
Isao Yamada
Keyword(s):  
Descent Method ◽  
Convex Minimization ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Hybrid Steepest Descent Method

scholarly journals The Hybrid Steepest Descent Method for Split Variational Inclusion and Constrained Convex Minimization Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jitsupa Deepho ◽  
Poom Kumam
Keyword(s):  
Descent Method ◽  
Convex Minimization ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Variational Inclusion ◽  
Common Element ◽  
Inclusion Problem ◽  
Constrained Convex Minimization ◽  
Hybrid Steepest Descent Method ◽  
Variational Inclusion Problem

We introduced an implicit and an explicit iteration method based on the hybrid steepest descent method for finding a common element of the set of solutions of a constrained convex minimization problem and the set of solutions of a split variational inclusion problem.

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.

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