TY - JOUR
T1 - On the behavior of the gradient norm in the steepest descent method
AU - Nocedal, Jorge
AU - Sartenaer, Annick
AU - Zhu, Ciyou
N1 - Funding Information:
∗Travel support for this research was provided by NATO grant CRG 960688. †This author was supported by National Science Foundation grant CDA-9726385 and by Department of Energy grant DE-FG02-87ER25047-A004. ∗∗Research Associate of the Belgian National Fund for Scientific Research.
PY - 2002/4
Y1 - 2002/4
N2 - 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.
AB - 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.
KW - Behavior of gradient norm
KW - Nonlinear optimization
KW - Steepest descent method
KW - Unconstrained optimization
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U2 - 10.1023/A:1014897230089
DO - 10.1023/A:1014897230089
M3 - Article
AN - SCOPUS:0036540507
VL - 22
SP - 5
EP - 35
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
SN - 0926-6003
IS - 1
ER -