Interpretation of the final_cost field in Ceres.
01 Jul 2022I love using the Ceres solver, but couldn’t figure out why when I computed the value of the cost function using my code, it was different from final_cost field of a Solver::Summary object.
Finally, I figured out that I constructed a cost function as
\[\sum_i \| f_i(x_i, \dots , x_{ik}) \|^2 \label{eqone}\]and in Ceres, the cost function is assumed to have this form, Ceres link:
\[\frac{1}{2}\sum_i \| f_i(x_i, \dots , x_{ik}) \|^2 \label{eqtwo}\]The only difference is that \(\frac{1}{2}\) in the Ceres version. To convert the final final_cost to my cost function, I need to multiply final_cost by two.
This was such a simple thing, but I spent more time than I would have liked figuring it out, so here this is as a TIL.