Keywords : line search

An Efficient Line Search Algorithm for Large Scale Optimization

Abbas Y. Al-Bayati; Ivan S. Latif

AL-Rafidain Journal of Computer Sciences and Mathematics, 2010, Volume 7, Issue 1, Pages 35-49
DOI: 10.33899/csmj.2010.163845

In this work we present a new algorithm of gradient descent type, in which the stepsize is computed by means of simple approximation of the Hessian Matrix to solve nonlinear unconstrained optimization function. The new proposed algorithm considers a new approximation of the Hessian based on the function values and its gradients in two successive points along the iterations one of them use Biggs modified formula to locate the new points. The corresponding algorithm belongs to the same class of superlinear convergent descent algorithms and it has been newly programmed to obtain the numerical results for a selected class of nonlinear test functions with various dimensions. Numerical experiments show that the new choice of the step-length required less computation work and greatly speeded up the convergence of the gradient algorithm especially, for large scaled unconstrained optimization problems.

A New Restarting Criterion for FR-CG Method with Exact and Inexact Line Searches

Maha S. Younis

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 95-110
DOI: 10.33899/csmj.2008.163975

A new restarting criterion for FR-CG method is derived and investigated in this paper. This criterion is globally convergent whenever the line search fulfills the Wolfe conditions. Our numerical tests and comparisons with the standard FR-CG method for large-scale unconstrained optimization are given, showining significantly improvements.