Relationship between the BFGS and conjugate gradient algorithms

Based upon analysis and numerical experience, the BFGS algorithm is currently considered to be one of the most effective algorithms for finding a minimum of an unconstrained function, f(x), x an element of IR/sup n/. However, when computer storage is at a premium, the usual alternative is to use a conjugate gradient (CG) method. This paper shows that the two algorithms are related to one another in a particularly close way. Based upon these observations, a new family of algorithms is proposed.