A stabilized version of the symmetric rank-one updating method for solving
unconstrained optimization problems is developed by introducing a scaling p
arameter to ensure that successive estimates of the inverse Hessian are pos
itive definite. The properties of this update are studied, and a new algori
thm based on this procedure is proposed. This algorithm uses Davidon's idea
of optimal conditioning in order to devise heuristics for selecting the sc
aling parameter automatically. Numerical testing shows that the new method
compares favourably with good implementations of the BFGS method. Thus it a
ppears very competitive in the class of methods which use only function and
gradient information.