On Steepest Descent Algorithms for Discrete Convex Functions

2004 ◽  
Vol 14 (3) ◽  
pp. 699-707 ◽  
Author(s):  
Kazuo Murota
Keyword(s):  
Convex Functions ◽  
Steepest Descent ◽  
Descent Algorithms ◽  
Discrete Convex

scholarly journals Proximity theorems of discrete convex functions

2004 ◽  
Vol 99 (3) ◽  
pp. 539-562 ◽  
Author(s):  
Kazuo Murota ◽  
Akihisa Tamura
Keyword(s):  
Convex Functions ◽  
Discrete Convex

A Study on the Optimal Double Parameters for Steepest Descent with Momentum

2015 ◽  
Vol 27 (4) ◽  
pp. 982-1004 ◽  
Author(s):  
Naimin Zhang
Keyword(s):  
Stability Analysis ◽  
Steepest Descent ◽  
Quadratic Functions ◽  
Optimal Parameters ◽  
Optimal Learning ◽  
Descent Algorithms ◽  
Learning Rates ◽  
Global Optimal ◽  
The Stability

This letter presents the stability analysis for two steepest descent algorithms with momentum for quadratic functions. The corresponding local optimal parameters in Torii and Hagan ( 2002 ) and Zhang ( 2013 ) are extended to the global optimal parameters, that is, both the optimal learning rates and the optimal momentum factors are obtained simultaneously which make for the fastest convergence.

Cone superadditivity of discrete convex functions

2011 ◽  
Vol 135 (1-2) ◽  
pp. 25-44 ◽  
Author(s):  
Yusuke Kobayashi ◽  
Kazuo Murota ◽  
Robert Weismantel
Keyword(s):  
Convex Functions ◽  
Discrete Convex
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