A new hyhbrid coefficient of conjugate gradient method

Abstract

<p><span>Hybridization is one of the popular approaches in modifying the conjugate gradient method. In this paper, a new hybrid conjugate gradient is suggested and analyzed in which the parameter <!--[if gte mso 9]><xml>
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 </xml><![endif]-->is evaluated as a convex combination of <!--[if gte mso 9]><xml>
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 </xml><![endif]--> while using exact line search. The proposed method is shown to possess both sufficient descent and global convergence properties. Numerical performances show that the proposed method is promising and has overpowered other hybrid conjugate gradient methods in its number of iterations and central processing unit per time. </span></p>

Interaction between updated FR-CG algorithms with optimal Cuckoo algorithm

“…Now we can consider that the formulas ( 10) and ( 11) are the first updated algorithm, and to develop them we add a third term to the new search direction of the format: (12) In the same way as the derivation of the parameter we derive the third term parameter as well:…”

“…Step 2: The best amount of step to algorithm results: set from SWC in (3), calculate the parameters used by the new 1 search direction (12)(13).…”

“…Zoutendijk [2] and Al-Baali [9]. Based on these theories in the previous article, many researchers have developed and updated the formulas of the correlation parameter as in [10][11][12][13][14][15][16][17][18]. "…”

A new hybrid conjugate gradient algorithm for unconstrained optimization with inexact line search

“…When implementated to general nonlinear function with inexact line searches, yet, the behavior of these methods is seeming different [14]. One of an important group of CG methods is the hybrid conjugate gradient algorithms, the hybrid computational schemes HCG work better than the classical CG methods because the HCG take the advantages of the two parameters [15].…”

An Efficient Hybrid Derivative-Free Projection Algorithm for Constraint Nonlinear Equations

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In this paper, by combining the Solodov and Svaiter projection technique with the conjugate gradient method for unconstrained optimization proposed by Mohamed et al (2020), we develop a derivative-free conjugate gradient method to solve nonlinear equations with convex constraints. The proposed method involves a spectral parameter that satisfies the sufficient descent condition.

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