A generalized conjugate gradient algorithm for minimization

Summary A generalized conjugate gradient algorithm which is invariant to a nonlinear scaling of a strictly convex quadratic function is described, which terminates after at mostn steps when applied to scaled quadratic functionsf: R _n R₁ of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andhC ¹ (R₁) an arbitrary strictly monotone functionh. The algorithm does not suppose the knowledge ofh orF but only off(x) and its gradientg(x).