From: Timo Heister Date: Tue, 19 Mar 2019 18:30:41 +0000 (-0600) Subject: step-15: doc update X-Git-Tag: v9.1.0-rc1~274^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=e9cd64520adbbaff38b818be928c0ef470336703;p=dealii.git step-15: doc update --- diff --git a/examples/step-15/doc/results.dox b/examples/step-15/doc/results.dox index 3fefe249fe..9aa5f0c173 100644 --- a/examples/step-15/doc/results.dox +++ b/examples/step-15/doc/results.dox @@ -137,7 +137,7 @@ Wolfe and Armijo-Goldstein conditions. For these, one can show the following: satisfied, i.e., the iteration never gets stuck as long as the problem is convex. - If we are close enough to the solution, then the conditions allow for - $\alpha^n$, thereby enabling quadratic convergence. + $\alpha^n=1$, thereby enabling quadratic convergence. We will not dwell on this here any further but leave the implementation of such algorithms as an exercise. We note, however, that when implemented @@ -146,6 +146,9 @@ problems can be solved in anywhere between 5 and 15 Newton iterations to engineering accuracy — substantially fewer than we need with the current version of the program. +More details on globalization methods including backtracking can be found, +for example, in Griva, Nash, Sofer: Linear and nonlinear optimization (2009). +

Integrating mesh refinement and nonlinear and linear solvers