Make sure we live what we preach.

diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib
index 2694ad09b919fa6071ba9555e21e727a8467d127..a2f213525ec3bf19c5419adb4d2a4b2c2933ccfc 100644 (file)
--- a/doc/doxygen/references.bib
+++ b/doc/doxygen/references.bib
@@ -251,6 +251,29 @@
 }
 
 
+%-------------------------------------------------------------------------------
+% Step 15
+%-------------------------------------------------------------------------------
+
+
+
+@Book{GNS08,
+  author =    {I. Griva and S. G. Nash and A. Sofer},
+  title =        {Linear and nonlinear optimization},
+  publisher =    {SIAM},
+  year =         2008,
+  edition =   {2nd}}
+
+@Book{NW99,
+  author =      {J. Nocedal and S. J. Wright},
+  title =       {Numerical Optimization},
+  publisher =   {Springer, New York},
+  year =        1999,
+  series =      {Springer Series in Operations Research}
+}
+
+
+
 %-------------------------------------------------------------------------------
 % Step 18
 %-------------------------------------------------------------------------------

diff --git a/examples/step-15/doc/results.dox b/examples/step-15/doc/results.dox
index 9aa5f0c173e17033370c8eea528e891a6ca960c7..ede6537f2e77d13060d422c108ffc6265a3ee053 100644 (file)
--- a/examples/step-15/doc/results.dox
+++ b/examples/step-15/doc/results.dox
@@ -93,7 +93,7 @@ We will discuss them in the following.
 <h4> Step length control </h4>
 
 Newton's method has two well known properties:
-- It does not converge from arbitrarily chosen starting points. Rather, a
+- It may not converge from arbitrarily chosen starting points. Rather, a
   starting point has to be close enough to the solution to guarantee
   convergence. However, we can enlarge the area from which Newton's method
   converges by damping the iteration using a <i>step length</i> 0<$\alpha^n\le
@@ -147,7 +147,19 @@ engineering accuracy &mdash; 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).
+for example, in @cite GNS08 and @cite NW99.
+
+A separate point, very much worthwhile making, however, is that in practice
+the implementation of efficient nonlinear solvers is about as complicated as
+the implementation of efficient finite element methods. One should not
+attempt to reinvent the wheel by implementing all of the necessary steps
+oneself. Rather, just like building finite element solvers on libraries
+such as deal.II, one should be building nonlinear solvers on libraries such
+as [SUNDIALS](https://computing.llnl.gov/projects/sundials). In fact,
+deal.II has interfaces to SUNDIALS and in particular to its nonlinear solver
+sub-package KINSOL through the SUNDIALS::KINSOL class. It would not be
+very difficult to base the current problem on that interface.
+
 
 
 <h4> Integrating mesh refinement and nonlinear and linear solvers </h4>