A convex combination conjugate gradient algorithm with application in mode function

Abstract

Conjugate gradient methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. In this paper, we suggest a new hybrid nonlinear conjugate gradient method, in which the conjugate gradient coefficient $\beta _{k}$ is a convex combination of $\beta _{k}^{NVHS^{\ast }}$ and $\beta _{k}^{DY}$. With the strong Wolfe line search, the descent property and global convergence of the new hybrid method are proved. The numerical results also show that our method is robust and efficient. Furthermore, the proposed algorithm was extended to solve the problem of mode function.