In this paper, a new spectral PRP conjugate gradient method is proposed, which can always generate sufficient descent direction without any line search. Under some standard conditions, global convergence of the proposed method is established when the standard Armijo or weak Wolfe line search is used. Moreover, we extend these results to the HS method. Numerical comparisons are reported with som...

A nonlinear conjugate gradient algorithm which is a modification of the Dai and Yuan [Y.H. Dai and Y, Yuan, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (1999), pp.177-182.] conjugate gradient algorithm satisfying a parametrized sufficient descent condition with a parameter k δ is proposed. The parameter k δ is computed by means of the conj...

Inspired by the large number of applications for symmetric nonlinear equations, this article will suggest two optimal choices modified Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) method minimizing measure function search direction matrix and combining proposed with default Newton direction. In addition, corresponding PRP parameters are incorporated Li Fukushima approximate to propose rob...

In this paper, we propose a modified Polak–Ribière–Polyak (PRP) conjugate gradient method. An attractive property of the proposed method is that the direction generated by the method is always a descent direction for the objective function. This property is independent of the line search used. Moreover, if exact line search is used, the method reduces to the ordinary PRP method. Under appropria...

In the cyclic Barzilai–Borwein (CBB) method, the same Barzilai–Borwein (BB) stepsize is reused for m consecutive iterations. It is proved that CBB is locally linearly convergent at a local minimizer with positive definite Hessian. Numerical evidence indicates that when m > n/2 3, where n is the problem dimension, CBB is locally superlinearly convergent. In the special case m = 3 and n = 2, it i...

The nonlinear conjugate gradient (CG) algorithm is a very effective method for optimization, especially for large-scale problems, because of its low memory requirement and simplicity. Zhang et al. (IMA J. Numer. Anal. 26:629-649, 2006) firstly propose a three-term CG algorithm based on the well known Polak-Ribière-Polyak (PRP) formula for unconstrained optimization, where their method has the s...

<p style='text-indent:20px;'>Tensor eigenvalue complementary problems, as a special class of are the generalization matrix problems in higher-order. In recent years, tensor complementarity have been studied extensively. The research fields mainly focus on analysis theory and algorithms. this paper, we investigate solution method for four kinds with different structures. By utilizing an eq...