Minimization of extended quadratic functions with inexact line searches

An algorithm for unconstrained minimization is proposed which is invariant to the nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and is designed for general use. It compares favorably in numerical tests (eight test functions, dimensionality up to 1000) with the 1975 Dixon algorithm on which this new algorithm is based.