On a class of Chebyshev approximation problems which arise in connection with a conjugate gradient type method

1986 ◽  
Vol 48 (5) ◽  
pp. 525-542 ◽  
Author(s):  
Roland Freund ◽  
Stephan Ruscheweyh
Keyword(s):  
Conjugate Gradient ◽  
Chebyshev Approximation ◽  
Type Method ◽  
Gradient Type ◽  
Approximation Problems

scholarly journals A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Can Li
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Optimization Problems ◽  
Gradient Methods ◽  
Type Method ◽  
Unconstrained Optimization Problems ◽  
Feasible Direction Method ◽  
Gradient Type ◽  
Large Scale Unconstrained Optimization ◽  
Nonnegative Constraints

We are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.

scholarly journals An efficient three-term conjugate gradient-type algorithm for monotone nonlinear equations

2020 ◽  
Author(s):  
Jamilu Sabi'u ◽  
Abdullah Shah
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Conjugate Gradient ◽  
Large Scale ◽  
Numerical Results ◽  
Search Direction ◽  
Projection Technique ◽  
Type Algorithm ◽  
Gradient Type

In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai-{L}iao condition and the descent three-term CG search direction. Both parameters are incorporated with the projection technique for solving large-scale monotone nonlinear equations. Using the Lipschitz and monotone assumptions, the global convergence of methods has been proved. Finally, numerical results are provided to illustrate the robustness of the proposed methods.

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