Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities

2003 ◽  
Vol 119 (1) ◽  
pp. 185-201 ◽  
Author(s):  
H. K. Xu ◽  
T. H. Kim
Keyword(s):  
Variational Inequalities ◽  
Steepest Descent ◽  
Descent Methods

Three-step relaxed hybrid steepest-descent methods for variational inequalities

2007 ◽  
Vol 28 (8) ◽  
pp. 1029-1036 ◽  
Author(s):  
Xie-ping Ding ◽  
Yen-cherng Lin ◽  
Jen-chih Yao
Keyword(s):  
Variational Inequalities ◽  
Steepest Descent ◽  
Descent Methods

scholarly journals Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian-Fen Gong ◽  
Dao-Jun Wen
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Common Fixed Points ◽  
Finite Family ◽  
Steepest Descent ◽  
Descent Methods ◽  
Pseudocontractive Mappings ◽  
Strictly Pseudocontractive Mappings

We modify the relaxed hybrid steepest-descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.

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