EFFICIENT IMPLEMENTATION OF A GENERALIZED POLAK-RIBIERE ALGORITHM FORNONLINEAR OPTIMIZATION

We have recently developed a new conjugate gradient type method, the G eneralized Polak-Ribiere (GPR) method, for unconstrained minimization. It is based on search directions that are parallel to the Newton dire ction of the restriction of the objective function f on the two dimens ional subspace span{-g,p}, with p a suitable direction in span{-g,s-}, where g and s- are the current gradient and previous search direction respectively. The new approach proved to be considerably more efficie nt than the original Polak-Ribiere method. In this paper, various impl ementations of the GPR method are compared with a currently available standard NAG software routine and also with the Nocedal, Buckley-LeNir and Shanno's limited memory algorithms. The results demonstrate the g eneral effectiveness of the new algorithm. We also give a very brief d iscussion of extensions of the GPR method that generate search directi ons parallel to Newton directions in subspaces of dimension greater th an two.