Unified approach to quadratically convergent algorithms for function minimization

In this paper, a unified method to construct quadratically convergent algorithms for function minimization is described. With this unified method, a generalized algorithm is derived. It is shown that all the existing conjugate-gradient algorithms and variable-metric algorithms can be obtained as particular cases. In addition, several new practical algorithms can be generated. The application of these algorithms to quadratic functions as well as nonquadratic functions is discussed.This research, supported by the Office of Scientific Research, Office of Aerospace Research, United States Air Force, Grant No. AF-AFOSR-828-67, is based on Ref. 1.