A More Lenient Stopping Rule for Line Search
Algorithms
An iterative univariate minimizer (line search) is often used to generate
a steplength in each step of a descent method for minimizing a
multivariate function. The line search performance strongly depends on
the choice of the stopping rule enforced. This termination criterion and
other algorithmic details also affect the overall efficiency of the
multivariate minimization procedure. Here we propose a more lenient
stopping rule for the convex in the bracketed search interval. We also
describe a remedy to special cases where the minimum point of the cubic
interpolant constructed in earch line search iteration is very close to
zero. Results in the context of the truncated Newton Package TNPACK for
18 standard test functions, as well as molecular potential functions, show
that these strategies can lead to modest performance improvements in
general, and significant improvements in special cases.
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