"On the Behavior of the Gradient Norm in the Steepest Descent Method "
J. Nocedal, A. Sartenaer, C. Zhu
Computational Optimization and Applications (May 2000).
It is well known that the norm of the gradient may be unreliable as a stopping test in unconstrained optimization, and that it often exhibits oscillations in the course of the optimization. In this paper we present results describing the properties of the gradient norm for the steepest descent method applied to quadratic objective functions. We also make some general observations that apply to nonlinear problems, relating the gradient norm, the objective function value, and the path generated by the iterates.