A GENERALIZED CONJUGATE-GRADIENT ALGORITHM

We present modifications of the generalized conjugate gradient algorit hm of Liu and Storey for unconstrained optimization problems (Ref. 1), extending its applicability to situations where the search directions are not defined. The use of new search directions is proposed and one additional condition is imposed on the inexact line search. The conve rgence of the resulting algorithm can be established under standard co nditions for a twice continuously differentiable function with a bound ed level set. Algorithms based on these modifications have been tested on a number of problems, showing considerable improvements. Compariso ns with the BFGS and other quasi-Newton methods are also given.