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Keywords:
unconstrained optimization; conjugate gradient method; descent direction; line search; image restoration
unconstrained optimization; conjugate gradient method; descent direction; line search; image restoration
Summary:
The conjugate gradient method is one of the most effective algorithm for unconstrained nonlinear optimization problems. This is due to the fact that it does not need a lot of storage memory and its simple structure properties, which motivate us to propose a new hybrid conjugate gradient method through a convex combination of $\beta _{k}^{RMIL}$ and $\beta _{k}^{HS}$. We compute the convex parameter $\theta _{k}$ using the Newton direction. Global convergence is established through the strong Wolfe conditions. Numerical experiments show the superior efficiency of our algorithm to solve unconstrained optimization problem compared to other considered methods. Applied to image restoration problem, our algorithm is competitive with existing algorithms and performs even better when the level of noise in the image is significant.
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