New six and seven-parameter family for CG-methods

Abstract EN

In this paper, we have investigated two new conjugacy coefficients for Conjugate Gradient (CG) methods for solving nonlinear unconstrained optimization.

First six-parameter family which depends on six parameters (λ, μ, ω, δ, γ, ϕ), second seven-parameter family which depends on seven parameters (λ, μ, ω, δ, γ, ϕ, ψ).

The clear feature of these two families is obtaining eleven or twelve different forms of original conjugacy coefficient from six and seven-parameter family, respectively.

The global convergence analysis of these two families had been proved.

Numerical results for these two families on some well-known test functions were reported and compared with the result of some well known formula for k β in CG-methods.