A descent family of Dai–Liao conjugate gradient methods Saman Babaie-Kafaki & Reza Ghanbari a Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran b School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran c Faculty of Mathematical Sciences, Ferdowsi Universi...

A. A new nonlinear conjugate gradient method, based on Perry’s idea, is presented. And it is shown that its sufficient descent property is independent of any line search and the eigenvalues of Pk+1Pk+1 are bounded above, where Pk+1 is the iteration matrix of the new method. Thus, the global convergence is proven by the spectral analysis for nonconvex functions when the line search fulfil...

Global convergence results are derived for well-known conjugate gradient methods in which the line search step is replaced by a step whose length is determined by a formula. The results include the following cases: 1. The Fletcher-Reeves method, the Hestenes-Stiefel method, and the Dai-Yuan method applied to a strongly convex LC objective function; 2. The Polak-Ribière method and the Conjugate ...

The Steepest descent method and the Conjugate gradient to minimize nonlinear functions have been studied in this work. Algorithms are presented implemented Matlab software for both methods. However, a comparison has made between method. obtained results time efficiency aspects. It is shown that needs fewer iterations more than On other hand, converges function less

<p>The conjugate gradient methods are noted to be exceedingly valuable for solving large-scale unconstrained optimization problems since it needn't the storage of matrices. Mostly parameter is focus methods. The current paper proposes new type solve optimization. A Hessian approximation in a diagonal matrix form on basis second and third-order Taylor series expansion was employed this stu...

We numerically analyze the possibility of turning off postsmoothing (relaxation) in geometric multigrid when used as a preconditioner in conjugate gradient linear and eigenvalue solvers for the 3D Laplacian. The geometric Semicoarsening Multigrid (SMG) method is provided by the hypre parallel software package. We solve linear systems using two variants (standard and flexible) of the preconditio...

In this paper, a new conjugate conjugate method with sufficient descent property is proposed for the unconstrained optimization problem. An attractive property of the new method is that the descent direction generated by the method always possess the sufficient descent property, and this property is independent of the line search used and the choice of ki  . Under mild conditions, the global c...