To the question of regularization of vector optimization problems

We propose the method of regularization of one class of vector optimizations problems in Banach spaces, in case where vector-valued mapping is not lower semicontinuous in certain sense, which implies violation of sufficient conditions of solvability.

An algorithm for constructing a direct and inverse operator of a real process

Consider the task of building a mathematical model of the real process, which translates the data at the entrance to a certain result at the output. Considered the case when severaldata is submitted to the entrance, and the output result is only one. The direct operator of the real process makes it possible to determine (provide) the result at the exit based on the known data at the entrance. The reverse operator on a known result on the way out of the real process allows you to find the necessary input. Operators of the real process are modeled with algebraic polynom to some extent. The degree of algebraic polynomic and its coefficients depend on a specific real process. Since input and output are known with some error in real-world processes, we take into account input and output errors when building operators. The task of building such operators is incorrect on Adamar, so we use the method of regularization of Tikhonov. This method allows you to build sustainable approach (taking into account the error of the input and output data) the right operators. The article examines in detail the algorithm for building a reverse operator. The direct operator algorithm is reviewed in the authors' previous article (link [2] in this article). Building a reverse operator comes down to solving a non-linear equation in an incorrect setting. The non-linear equation is solved by Newton's iterative method. The software implementation of the algorithm has been carried out. Three test examples are considered, which confirm the correctness of the algorithm and program. The algorithm can be summarized in case there are several data (at least two) at both the entrance and exit.

Diffraction of the field of vertical electric dipole on the spiral conductive sphere in the presence of a cone

The problem of diffraction of a vertical electric dipole field on a spiral conductive sphere and a cone has been solved. By the method of regularization of the matrix operator of the problem, an infinite system of linear algebraic equations of the second kind with a compact matrix operator in Hilbert space $\ell_2$ is obtained. Some limiting variants of the problem statement are considered.

On monotone ill-posed problems in Hilbert spaces

The main aim of this paper is to study convergence rates for an operator method of regularization to solve nonlinear ill-posed problems involving monotone operators in infinite-dimentional Hilbert space without needing closeness conditions. Then these results are presented in form of combination with finite-dimentional approximations of the space. An iterative method for solving regularized equation is given and an example in the theory of singular integral equations is considered for illustration.

A Reverse Solving Method of Regularization on the Calculation of Acoustic Field

Based on the normalization of sample datas errors, a feasible reverse solving method of regularization is studied to avoid ill-posed problem in inverse problem. The analysis result shows that the high robustness in selection method of regularization parameters, rather than the strategy of regularization, is the key factor deciding the effectiveness of regularization.