International Scholarly Research Notices

Research Article

A Descent Dai-Liao Conjugate Gradient Method Based on a Modified Secant Equation and Its Global Convergence

Algorithm 1

(MDL-CG).
1. Choose an initial point 𝑥 0 ∈ ℝ 𝑛 ; Set 𝑘 = 0 .
2. If ‖ 𝑔 𝑘 ‖ = 0 , then terminate; Otherwise go to the next.
3. Compute the descent direction 𝑑 𝑘 by (15) and (17).
4. Determine a stepsize 𝛼 𝑘 by some line search rule.
5. Let 𝑥 𝑘 + 1 = 𝑥 𝑘 + 𝛼 𝑘 𝑑 𝑘 .
6. Set 𝑘 = 𝑘 + 1 and go to 2.