The method of steepest descent for solving unconstrained minimization problems is well understood. It is known, for instance, that when applied to a smooth objective function f, and converging to a solution point x where the corresponding Hessian matrix F(x) is positive definite, the asymptotic...

A new criterion is introduced for comparing the convergence properties of variable metric algorithms, focusing on stepwise descent properties. This criterion is a bound on the rate of decrease in the function value at each iterative step (single-step convergence rate). Using this criterion as a...