Abstract
In this paper, we develop a new hybrid conjugate gradient method that inherits the features of the Liu and Storey (LS), Hestenes and Stiefel (HS), Dai and Yuan (DY) and Conjugate Descent (CD) conjugate gradient methods. The new method generates a descent direction independently of any line search and possesses good convergence properties under the strong Wolfe line search conditions. Numerical results show that the proposed method is robust and efficient.
Highlights
In this paper, we consider solving the unconstrained optimization problem min f (x), (1)where x ∈ Rn is an n-dimensional real vector and f ∶ Rn → R is a smooth function, using a nonlinear conjugate gradient method
The authors showed that the method satisfies the sufficient descent condition and possesses global convergence property under the strong Wolfe line search
Huang et al [17] proved that the WYL k method satisfies the sufficient descent property and established that the method is globally convergent under the strong Wolfe line search if the parameter in (5) satisfies σ
Summary
We consider solving the unconstrained optimization problem min f (x),. Where x ∈ Rn is an n-dimensional real vector and f ∶ Rn → R is a smooth function, using a nonlinear conjugate gradient method. To solve problem (1), a nonlinear conjugate gradient method starts with an initial guess, x0 ∈ Rn , and generates a sequence {xk}∞k=0 using the recurrence xk+1 = xk + kdk,. The strong Wolfe line search f (xk + kdk) ≤ f (xk) + |gTk+1dk| ≤ |gTk dk|, kgTk dk (5). The generalized Wolfe conditions f (xk + kdk) ≤ f (xk) + kgTk dk gTk dk ≤ gTk+1dk ≤ − 1gTk dk,. Conjugate gradient methods differ by the choice of the coefficient k. The first category includes Fletcher and Reeves (FR) [11], Dai and Yuan (DY) [6] and Conjugate Descent (CD) [10]: FR k
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