AL-Rafidain Journal of Computer Sciences and Mathematics

This paper develops a special conjugate gradient algorithm for solving  unconstrained minimized problems. This development can be regarded as some kind of convex combination of the MPR and MLS methods.  Experimental results indicate that the new algorithm is more efficient than the Polak and Ribiere - algorithm.
 

Conjugate gradient methods are wildly used for unconstrained optimization especially when the dimension is large. In this paper we propose a new kind of nonlinear conjugate gradient methods which on the study of Dai and Liao (2001), the new idea is how to use the pair conjugate gradient method with this study (new cojugacy condition) which consider an inexact line search scheme but reduce to the old one if the line search is exact. Convergence analysis for this new method is provided. Our numerical results show that this new methods is very efficient for the given ten test function compared with other methods.
 

We consider a class of invariant Hyperbolic scaling of a strictly convex quadratic function, to extend the family of the conjugate gradient methods for solving unconstrained minimization problems. An algorithm is derived and evaluated numerically. The results indicate that, in general, the new algorithm is superior to the classical standard CG-algorithm.
 

A new non-quadratic model is proposed for solving unconstrained optimization problems, which modifies and develops the classical conjugate gradient methods. The technique has the same properties as the classical conjugate gradient method that can be applied to a quadratic function. An algorithm is derived and evaluated numerically for some standard test functions .The results indicate that, in general, the new algorithm is an improvement on the previous methods so it remains to be investigated.