  A general framework for solving nonlinear least squares problems without the
employment of derivatives is proposed in the present paper together with a new
general global convergence theory. With the aim to cope with the case in which
the number of variables is big (for the standards of derivative-free
optimization), two dimension-reduction procedures are introduced. One of them
is based on iterative subspace minimization and the other one is based on
spline interpolation with variable nodes. Each iteration based on those
procedures is followed by an acceleration step inspired in the Sequential
Secant Method. The practical motivation for this work is the estimation of
parameters in Hydraulic models applied to dam breaking problems. Numerical
examples of the application of the new method to those problems are given.
