Various documentation fixes from William Rucklidge. Change-Id: I102e98f41f4b5fe2a84d1224d5ed7517fdfdb022
diff --git a/docs/source/modeling.rst b/docs/source/modeling.rst index 5fff351..21cda70 100644 --- a/docs/source/modeling.rst +++ b/docs/source/modeling.rst
@@ -43,7 +43,7 @@ outliers on the solution of non-linear least squares problems. :math:`l_j` and :math:`u_j` are lower and upper bounds on the -:math:parameter block `x_j`. +parameter block :math:`x_j`. As a special case, when :math:`\rho_i(x) = x`, i.e., the identity function, and :math:`l_j = -\infty` and :math:`u_j = \infty` we get @@ -1462,7 +1462,7 @@ .. function bool Problem::HasParameterBlock(const double* values) const; - Is the give parameter block present in the problem or not? + Is the given parameter block present in the problem or not? .. function void Problem::GetParameterBlocks(vector<double*>* parameter_blocks) const
diff --git a/docs/source/solving.rst b/docs/source/solving.rst index 4d091a3..1b52c02 100644 --- a/docs/source/solving.rst +++ b/docs/source/solving.rst
@@ -27,13 +27,18 @@ L \le x \le U :label: nonlinsq -Here, the Jacobian :math:`J(x)` of :math:`F(x)` is an :math:`m\times -n` matrix, where :math:`J_{ij}(x) = \partial_j f_i(x)` and the -gradient vector :math:`g(x) = \nabla \frac{1}{2}\|F(x)\|^2 = J(x)^\top -F(x)`. Since the efficient global minimization of :eq:`nonlinsq` for +Where, :math:`L` and :math:`U` are lower and upper bounds on the +parameter vector :math:`x`. + +Since the efficient global minimization of :eq:`nonlinsq` for general :math:`F(x)` is an intractable problem, we will have to settle for finding a local minimum. +In the following, the Jacobian :math:`J(x)` of :math:`F(x)` is an +:math:`m\times n` matrix, where :math:`J_{ij}(x) = \partial_j f_i(x)` +and the gradient vector is :math:`g(x) = \nabla \frac{1}{2}\|F(x)\|^2 += J(x)^\top F(x)`. + The general strategy when solving non-linear optimization problems is to solve a sequence of approximations to the original problem [NocedalWright]_. At each iteration, the approximation is solved to @@ -118,7 +123,7 @@ giving rise to a different concrete trust-region algorithm. Currently Ceres, implements two trust-region algorithms - Levenberg-Marquardt and Dogleg, each of which is augmented with a line search if bounds -constrained are present [Kanzow]_. The user can choose between them by +constraints are present [Kanzow]_. The user can choose between them by setting :member:`Solver::Options::trust_region_strategy_type`. .. rubric:: Footnotes