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.

Keywords: nonlinear integro-differential equations, descent algorithm, regularization, genetic algorithm

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