Hierarchical Convex Optimization by the Hybrid Steepest Descent Method with Proximal Splitting Operators—Enhancements of SVM and Lasso

2019 ◽  
pp. 413-489 ◽  
Author(s):  
Isao Yamada ◽  
Masao Yamagishi
Keyword(s):  
Convex Optimization ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Hybrid Steepest Descent Method

A hybrid steepest descent method for constrained convex optimization

Automatica ◽  
2009 ◽  
Vol 45 (2) ◽  
pp. 525-531 ◽  
Author(s):  
Mathieu Gerard ◽  
Bart De Schutter ◽  
Michel Verhaegen
Keyword(s):  
Convex Optimization ◽  
Descent Method ◽  
Steepest Descent ◽  
Steepest Descent Method ◽  
Hybrid Steepest Descent Method ◽  
Constrained Convex Optimization

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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