Convergence of a two-parameter family of conjugate gradient methods with a fixed formula of stepsize

Abstract

We prove the global convergence of a two-parameter family of conjugate gradient methods that use a new and different formula of stepsize from Wu \cite% {14}. Numerical results are presented to confirm the effectiveness of the proposed stepsizes by comparing with the stepsizes suggested by Sun and his colleagues \cite% {2, 12}.\\

Keywords

• unconstrained optimization
• conjugate gradient methods
• global convergence
• stepsize
• line search