We present an automatic blocking algorithm for some medium size nonlinear least squares problems that arise in the inversion of travel time data in geophysics. This blocking leads to a nonlinear Gauss-Seidel type iteration which can be distributed to a network of computers. The low dimensional blocks are also amenable to global optimization methods which leads to further parallelization. All this is necessary because the original problem is generally non- convex, ill-conditioned, with a goal functional that is very expensive to evaluate.
Victor L. Pereyra,
"Parallel block inversion of geophysical data", Proc. SPIE 2033, Mathematical Methods in Geophysical Imaging, (1 December 1993); doi: 10.1117/12.164838; https://doi.org/10.1117/12.164838