Scaled conjugate gradient algorithms for unconstrained optimization

In this work we present and analyze a new scaled conjugate gradient algorithm and its implementation, based on an interpretation of the secant equation and on the inexact Wolfe line search conditions. The best spectral conjugate gradient algorithm SCG by Birgin and Martinez (2001), which is mainly a scaled variant of Perry's (1977), is modified in such a manner to overcome the lack of positive definiteness of the matrix defining the search...