Abstract
One adaptive choice for the parameter of the Dai–Liao conjugate gradient method is suggested in this paper, which is obtained with modified quasi–Newton equation. So we get a modified Dai–Liao conjugate gradient method. Some interesting features of the proposed method are introduced: (i) The value of parameter t of the modified Dai–Liao conjugate gradient method takes both the gradient and function value information. (ii) We establish the global convergence property of the modified Dai–Liao conjugate gradient method under some suitable assumptions. (iii) Numerical results show that the modified DL method is effective in practical computation and the image restoration problems.
Highlights
In this paper, we consider the following unconstrained optimization problem: min f(x), x ∈ Rn, (1)where f: Rn ⟶ R and f is a continuously differentiable function
In order to ensure general functions satisfy global convergence, a new formula was presented by Dai and Liao as follows: βDk L+
Some scholars tried to find the new choice for the nonnegative parameter t in (13) [24, 25]. e remainder of this paper is organized as follows: in Section 2, based on the new conjugacy condition, a modified DL gradient method is proposed with a new value for the parameter
Summary
We consider the following unconstrained optimization problem: min f(x), x ∈ Rn,. Erefore, in recent year, many scholars try to research some modified formulas for conjugate gradient methods which have global convergence property for general functions and satisfied performance in the numerical test. Dai and Liao [20] proposed some modified conjugate methods with a new conjugacy condition Their method cited in [20] has global convergence for general function, and has better numerical performance than HS and PR methods. In order to ensure general functions satisfy global convergence, a new formula was presented by Dai and Liao as follows: βDk L+. E remainder of this paper is organized as follows: in Section 2, based on the new conjugacy condition, a modified DL gradient method is proposed with a new value for the parameter.
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