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

Abstract

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.