scholarly journals Condition Numbers, the Barrier Method, and the Conjugate-Gradient Method

1996 ◽  
Vol 6 (4) ◽  
pp. 879-912 ◽  
Author(s):  
James Renegar
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Condition Numbers ◽  
Barrier Method

MATRIX ANALYSES ON THE DAI–LIAO CONJUGATE GRADIENT METHOD

2019 ◽  
Vol 61 (02) ◽  
pp. 195-203
Author(s):  
Z. AMINIFARD ◽  
S. BABAIE-KAFAKI
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Search Direction ◽  
Condition Numbers ◽  
Test Problems ◽  
Spectral Condition ◽  
Testing Environment ◽  
Measure Function ◽  
Descent Property

Some optimal choices for a parameter of the Dai–Liao conjugate gradient method are proposed by conducting matrix analyses of the method. More precisely, first the $\ell _{1}$ and $\ell _{\infty }$ norm condition numbers of the search direction matrix are minimized, yielding two adaptive choices for the Dai–Liao parameter. Then we show that a recent formula for computing this parameter which guarantees the descent property can be considered as a minimizer of the spectral condition number as well as the well-known measure function for a symmetrized version of the search direction matrix. Brief convergence analyses are also carried out. Finally, some numerical experiments on a set of test problems related to constrained and unconstrained testing environment, are conducted using a well-known performance profile.

Sign in / Sign up

Export Citation Format

Share Document