Imperfect conjugate gradient algorithms for extended quadratic functions

Summary Generalized conjugate gradient algorithms which are invariant to a nonlinear scaling of a strictly convex quadratic function are described. The algorithms when applied to scaled quadratic functionsfR _n R ₁ of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andhC ¹(R ₁) an arbitrary strictly monotone functionh generate the same direction vectors as for the functionF without perfect steps.