We consider gradient algorithms for minimizing a quadratic function in R with large n. We suggest a particular sequence of step-lengthes and demonstrate that the resulting gradient algorithm has a convergence rate comparable with that of Conjugate Gradients and other methods based on the use of Krylov spaces. When the problem is large and sparse, the proposed algorithm can be more efficient tha...

Conjugate gradient algorithms are very powerful methods for solving large-scale unconstrained optimization problems characterized by low memory requirements and strong local and global convergence properties. Over 25 variants of different conjugate gradient methods are known. In this paper we propose a fundamentally different method, in which the well known parameter k β is computed by an appro...

In this paper we explore different strategies to guide backpropagation algorithm used for training artificial neural networks. Two different variants of steepest descent-based backpropagation algorithm, and four different variants of conjugate gradient algorithm are tested. The variants differ whether or not the time component is used, and whether or not additional gradient information is utili...

On the Convergence Rate of Variants Conjugate Gradient Algorithm in Finite Precision Arithmetic

In this paper, we proposed a new hybrid conjugate gradient algorithm for solving unconstrained optimization problems as convex combination of the Dai-Yuan algorithm, conjugate-descent and Hestenes-Stiefel algorithm. This is globally convergent satisfies sufficient descent condition by using strong Wolfe conditions. The numerical results show that nonlinear efficient robust.

In this paper‎, ‎two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS})‎ ‎conjugate gradient method are presented to solve unconstrained optimization problems‎. ‎A remarkable property of the proposed methods is that the search direction always satisfies‎ ‎the sufficient descent condition independent of line search method‎, ‎based on eigenvalue analysis‎. ‎The globa...

Although quasi-Newton algorithms generally converge in fewer iterations than conjugate gradient algorithms, they have the disadvantage of requiring substantially more storage. An algorithm will be described which uses an intermediate (and variable) amount of storage and which demonstrates convergence which is also intermediate, that is, generally better than that observed for conjugate gradient...

 Abstract: This study deals with modeling of heat flux at the external surface of combustion chamber wall in an internal combustion (IC) engine as a function of crank angle. This investigation results in an inverse heat conduction problem in the cylinder wall. Alifanov regularization method is used for solving this inverse problem. This problem study as an optimization problem in which a square...

Abstract: The conjugate gradient method is an algorithm for the numerical solution of systems of linear equations whose matrices are positive-definite and symmetric. It is an iterative method that can even be applied to solve a sparse system of equations. In this paper, we applied the conjugate gradient method of higher order to wave propagation control problems. The algorithm of this method wa...

We combine linear algebra techniques with finite element techniques to obtain a reliable stopping cri-terion for Krylov method based algorithms. The Conjugate Gradient method has for a long time beensuccessfully used in the solution of the symmetric and positive definite systems obtained from thefinite-element approximation of self-adjoint elliptic partial differential equations...