Backtracking line searches are subsolvers that can be specified in the
line_search attribute of a NewtonSolver, and are used to pull back to a reasonable point when a Newton step goes too far. This can occur when a step causes output variables to exceed their specified lower and upper bounds. It can also happen in more complicated problems where a full Newton step happens to take you well past the nonlinear solution, even to an area where the residual norm is worse than the initial point. Specifying a value for line_search can help alleviate these problems and improve robustness of your Newton solve.
There are two different backtracking line-search algorithms in OpenMDAO: