Search

Abstract: In this paper, we consider the Polak–Ribière (or Polak–Ribière plus) conjugate gradient method for solving optimality condition of an unconstrained minimization problem. We give two new steplength rules only using gradient, and under gradient-Lipschitz assumption prove this method’s global convergence correspondingly. Then, we develop a practical Polak–Ribière plus method whose steplength is located by one inequality only using gradient, and report promising numerical results on high accuracy solution for some standard test problems when compared to the state-of-art methods in this research direction. Importantly, our work provides a new idea of devising a practical version of the celebrated Polak–Ribière (or Polak–Ribière plus) method. [Copyright &y& Elsevier]

Abstract: Nonlinear conjugate gradient (CG) methods have played an important role in solving large-scale unconstrained optimization. Their wide application in many fields is due to their low memory requirements and global convergence properties. Numerous studies and modifications have been conducted recently to improve this method. In this paper, a new class of conjugate gradient coefficients (βk ) that possess global convergence properties is presented. The global convergence result is established using exact line searches. Numerical result shows that the proposed formula is superior and more efficient when compared to other CG coefficients. [Copyright &y& Elsevier]

Sufficient descent condition is very crucial in establishing the global convergence of nonlinear conjugate gradient method. In this paper, we modified two conjugate gradient methods such that both methods satisfy this property. Under suitable conditions, we prove the global convergence of the proposed methods. Numerical results show that the proposed methods are efficient for the given test problems. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, a new spectral PRP conjugate gradient algorithm has been developed for solving unconstrained optimization problems, where the search direction was a kind of combination of the gradient and the obtained direction, and the steplength was obtained by the Wolfe-type inexact line search. It was proved that the search direction at each iteration is a descent direction of objective function. Under mild conditions, we have established the global convergence theorem of the proposed method. Numerical results showed that the algorithm is promising, particularly, compared with the existing several main methods. [ABSTRACT FROM AUTHOR]

Abstract: A modified conjugate gradient method is presented for solving unconstrained optimization problems, which possesses the following properties: (i) The sufficient descent property is satisfied without any line search; (ii) The search direction will be in a trust region automatically; (iii) The Zoutendijk condition holds for the Wolfe–Powell line search technique; (iv) This method inherits an important property of the well-known Polak–Ribière–Polyak (PRP) method: the tendency to turn towards the steepest descent direction if a small step is generated away from the solution, preventing a sequence of tiny steps from happening. The global convergence and the linearly convergent rate of the given method are established. Numerical results show that this method is interesting. [Copyright &y& Elsevier]