In [Z.Wei, S. Yao, L. Liu, The convergence properties of some new conjugate gradient methods, Applied Mathematics and Computation 183 (2006) 1341–1350], Wei et al. proposed a new conjugate gradient method called WYL method which has good numerical experiments and some excellent properties such as b k P 0. In this paper, we prove that while tk 6 1 c 2L kgkk kdkk , the sufficient descent conditio...

Conjugate gradient methods are probably the most famous iterative methods for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. In this paper, we propose a new conjugate gradient method which is based on the MBFGS secant condition by modifying Perry’s method. Our proposed met...

<span>In this article, we give a new modification for the Dai-Liao method to solve monotonous nonlinear problems. In our modification, relied on two important procedures, one of them was projection and second damping quasi-Newton condition. The approach derivation yields parameters conjugated gradient direction which, through some conditions, have demonstrated sufficient descent property ...

Abstract The aim of this paper is to prove the theorem which generates many examples functions belonging a geometrically defined class uniformly starlike introduced by Goodman in 1991. Only very few explicit were known until now. Next we obtain inclusion relations between some subclasses convex and functions.

Abstract This paper discusses an active set trust-region algorithm for bound-constrained optimization problems. A sufficient descent condition is used as a computational measure to identify whether the function value reduced or not. To get our complexity result, critical which computationally better than other known measures. Under positive definiteness of approximated Hessian matrices restrict...