scholarly journals Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization

2019 ◽  
Vol 75 (1) ◽  
pp. 169-205
Author(s):  
C. P. Brás ◽  
J. M. Martínez ◽  
M. Raydan
Keyword(s):  
Unconstrained Optimization ◽  
Large Scale ◽  
Subspace Minimization ◽  
Large Scale Unconstrained Optimization ◽  
Matrix Free

scholarly journals Several Guaranteed Descent Conjugate Gradient Methods for Unconstrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
San-Yang Liu ◽  
Yuan-Yuan Huang
Keyword(s):  
Unconstrained Optimization ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Gradient Methods ◽  
Numerical Results ◽  
Conjugate Gradient Methods ◽  
Descent Condition ◽  
Wolfe Line Search ◽  
Large Scale Unconstrained Optimization

This paper investigates a general form of guaranteed descent conjugate gradient methods which satisfies the descent conditiongkTdk≤-1-1/4θkgk2  θk>1/4and which is strongly convergent whenever the weak Wolfe line search is fulfilled. Moreover, we present several specific guaranteed descent conjugate gradient methods and give their numerical results for large-scale unconstrained optimization.

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