Geodesic
A quasi-Newton two-step method for the residual function minimization
Numerical methods and programming, Tome 10 (2009) no. 1, pp. 75-82

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A quasi-Newton two-step method is proposed for the minimization of a residual function with consideration of the raviness of the function being minimized. At each iteration of this method, the parameters are displaced in two steps. This allows one to get around the bends of the ravine bottom and to accelerate the minimization process. The method is used to solve numerically a model problem of hydraulic conductivity identification for a three-dimensional anisotropic confined aquifer and to minimize several test functions. The efficiency of the two-step method is shown in comparison with one of the versions of the Levenberg-Marquardt method.
Keywords: minimization of residual function; inverse problem. 
@article{VMP_2009_10_1_a8,
     author = {P. A. Mazurov and A. V. Elesin and A. Sh. Kadyrova},
     title = {A {quasi-Newton} two-step method for the residual function minimization},
     journal = {Numerical methods and programming},
     pages = {75--82},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a8/}
}
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P. A. Mazurov; A. V. Elesin; A. Sh. Kadyrova. A quasi-Newton two-step method for the residual function minimization. Numerical methods and programming, Tome 10 (2009) no. 1, pp. 75-82. http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a8/