Paper ID sheet
- TITLE: Convergence of the Iterates of Descent Methods for
Analytic Cost Functions
- AUTHORS: P.-A. Absil, R. Mahony, B. Andrews.
In the early eighties Lojasiewicz proved that a bounded solution of a
gradient flow for an analytic cost function converges to a
well-defined limit point. In this paper, we show that the iterates of
numerical descent algorithms, for an analytic cost function, share
this convergence property if they satisfy certain natural descent
conditions. The results obtained are applicable to a broad class of
optimization schemes and strengthen classical ``weak convergence''
results for descent methods to ``strong limit-point convergence'' for a
large class of cost functions of practical interest. The result does
not require that the cost has isolated critical points, requires no
assumptions on the convexity of the cost, nor any non-degeneracy
conditions on the Hessian of the cost at critical points.
SIAM Journal on Optimization, Vol. 16, No. 2, pp. 531-547, 2005.
- DATE OF ENTRY: March 2004.
author = "Absil, P.-A. and Mahony, R. and Andrews, B.",
title = "Convergence of the Iterates of Descent Methods for Analytic Cost Functions",
journal = "SIAM J. Optim.",
year = 2005,
volume = 6,
number = 2,
pages = "531--547",