diff --git a/docs/source/gradient_solver.rst b/docs/source/gradient_solver.rst
index cf06530..1ef1515 100644
--- a/docs/source/gradient_solver.rst
+++ b/docs/source/gradient_solver.rst
@@ -327,11 +327,10 @@
 
    Solver terminates if
 
-   .. math:: \frac{|\Delta \text{cost}|}{\text{cost}} < \text{function_tolerance}
+   .. math:: \frac{|\Delta \text{cost}|}{\text{cost}} <= \text{function_tolerance}
 
    where, :math:`\Delta \text{cost}` is the change in objective
-   function value (up or down) in the current iteration of
-   Levenberg-Marquardt.
+   function value (up or down) in the current iteration of the line search.
 
 .. member:: double GradientProblemSolver::Options::gradient_tolerance
 
@@ -339,13 +338,24 @@
 
    Solver terminates if
 
-   .. math:: \|x - \Pi \boxplus(x, -g(x))\|_\infty < \text{gradient_tolerance}
+   .. math:: \|x - \Pi \boxplus(x, -g(x))\|_\infty <= \text{gradient_tolerance}
 
    where :math:`\|\cdot\|_\infty` refers to the max norm, :math:`\Pi`
    is projection onto the bounds constraints and :math:`\boxplus` is
    Plus operation for the overall local parameterization associated
    with the parameter vector.
 
+.. member:: double GradientProblemSolver::Options::parameter_tolerance
+
+   Default: ``1e-8``
+
+   Solver terminates if
+
+   .. math:: \|\Delta x\| <= (\|x\| + \text{parameter_tolerance}) * \text{parameter_tolerance}
+
+   where :math:`\Delta x` is the step computed by the linear solver in
+   the current iteration of the line search.
+
 .. member:: LoggingType GradientProblemSolver::Options::logging_type
 
    Default: ``PER_MINIMIZER_ITERATION``
diff --git a/docs/source/nnls_solving.rst b/docs/source/nnls_solving.rst
index 95f1a36..d3a6479 100644
--- a/docs/source/nnls_solving.rst
+++ b/docs/source/nnls_solving.rst
@@ -1156,7 +1156,7 @@
 
    Solver terminates if
 
-   .. math:: \frac{|\Delta \text{cost}|}{\text{cost}} < \text{function_tolerance}
+   .. math:: \frac{|\Delta \text{cost}|}{\text{cost}} <= \text{function_tolerance}
 
    where, :math:`\Delta \text{cost}` is the change in objective
    function value (up or down) in the current iteration of
@@ -1168,7 +1168,7 @@
 
    Solver terminates if
 
-   .. math:: \|x - \Pi \boxplus(x, -g(x))\|_\infty < \text{gradient_tolerance}
+   .. math:: \|x - \Pi \boxplus(x, -g(x))\|_\infty <= \text{gradient_tolerance}
 
    where :math:`\|\cdot\|_\infty` refers to the max norm, :math:`\Pi`
    is projection onto the bounds constraints and :math:`\boxplus` is
@@ -1181,10 +1181,10 @@
 
    Solver terminates if
 
-   .. math:: \|\Delta x\| < (\|x\| + \text{parameter_tolerance}) * \text{parameter_tolerance}
+   .. math:: \|\Delta x\| <= (\|x\| + \text{parameter_tolerance}) * \text{parameter_tolerance}
 
    where :math:`\Delta x` is the step computed by the linear solver in
-   the current iteration of Levenberg-Marquardt.
+   the current iteration.
 
 .. member:: LinearSolverType Solver::Options::linear_solver_type
 
diff --git a/internal/ceres/line_search_minimizer.cc b/internal/ceres/line_search_minimizer.cc
index 0d29b3e..62264fb 100644
--- a/internal/ceres/line_search_minimizer.cc
+++ b/internal/ceres/line_search_minimizer.cc
@@ -412,7 +412,7 @@
 
     const double absolute_function_tolerance =
         options.function_tolerance * previous_state.cost;
-    if (fabs(iteration_summary.cost_change) < absolute_function_tolerance) {
+    if (fabs(iteration_summary.cost_change) <= absolute_function_tolerance) {
       summary->message =
           StringPrintf("Function tolerance reached. "
                        "|cost_change|/cost: %e <= %e",
diff --git a/internal/ceres/trust_region_minimizer.cc b/internal/ceres/trust_region_minimizer.cc
index e490768..d654d08 100644
--- a/internal/ceres/trust_region_minimizer.cc
+++ b/internal/ceres/trust_region_minimizer.cc
@@ -489,7 +489,7 @@
       iteration_summary.cost_change =  cost - new_cost;
       const double absolute_function_tolerance =
           options_.function_tolerance * cost;
-      if (fabs(iteration_summary.cost_change) < absolute_function_tolerance) {
+      if (fabs(iteration_summary.cost_change) <= absolute_function_tolerance) {
         summary->message =
             StringPrintf("Function tolerance reached. "
                          "|cost_change|/cost: %e <= %e",