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A general framework for solving nonlinear least squares problems without theemployment of derivatives is proposed in the present paper together with a newgeneral global convergence theory. With the aim to cope with the case in whichthe number of variables is big (for the standards of derivative-freeoptimization), two dimension-reduction procedures are introduced. One of themis based on iterative subspace minimization and the other one is based onspline interpolation with variable nodes. Each iteration based on thoseprocedures is followed by an acceleration step inspired in the SequentialSecant Method. The practical motivation for this work is the estimation ofparameters in Hydraulic models applied to dam breaking problems. Numericalexamples of the application of the new method to those problems are given.

Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients