Fix a bug in inner iterations

Normally we expect it to be the case that inner iteration cost
will be less than the trust region cost, but due to round off
error it can be that it is larger, so make the test for inner
iteration being successful to be stricter.

Change-Id: Icbafe9fc6a311940d5368cca78eeac7ccd5fa943

internal/ceres/trust_region_minimizer.cc

diff --git a/internal/ceres/trust_region_minimizer.cc b/internal/ceres/trust_region_minimizer.cc
index 068cc8d..c2c10f8 100644
--- a/internal/ceres/trust_region_minimizer.cc
+++ b/internal/ceres/trust_region_minimizer.cc
@@ -562,7 +562,13 @@
   const double inner_iteration_cost_change =
       candidate_cost_ - inner_iteration_cost;
   model_cost_change_ += inner_iteration_cost_change;
-  inner_iterations_were_useful_ = inner_iteration_cost < x_cost_;
+
+  // Make sure that the inner iteration has improved over both the current
+  // (x_cost_) and the trust region step cost (candidate_cost). In exact
+  // arithmetic we would expect that inner iterations cost can't possibly be
+  // worse than candidate_cost, but in finite precision this can happen due to
+  // round-off error. So, we check that we improve upon the minimum of both.
+  inner_iterations_were_useful_ = inner_iteration_cost < std::min(x_cost_, candidate_cost_);
   const double inner_iteration_relative_progress =
       1.0 - inner_iteration_cost / candidate_cost_;