Minimization of the residual functional in problems of stream experimental data processing

B. G. Shpynev ; A. L. Voronov

Numerical methods and programming, Tome 14 (2013) no. 4, pp. 503-515.

Résumé

We consider the problem of residual functional minimization that arises in the case of long experimental data series processing when the measured process is described by nonlinear integro-differential or integral equations. For the nonlinear inverse problems that deal with functions with continuous first and second derivatives on a compact set, we consider the three main techniques: a descent algorithm, a regularization method, and the search of the optimal solution in the set of all suboptimal solutions. The central part of the new method is the descent algorithm, which works on a multidimensional net constructed on the base of polytope vertices. The regularization of the solution is performed using the Sobolev's space as a minimization domain. To avoid the ambiguities due to the presence of suboptimal solutions, we apply a special technique that uses the elements of genetic algorithms and allows one to adopt the previously obtained processing results.

Détail

Keywords: nonlinear integro-differential equations; descent algorithm; regularization; genetic algorithm.