Regularized dual method for nonlinear mathematical programming

Near-field inverse scattering problems in noninvasive diagnostics of subsurface dielectric structures

“…At that, the modified Lagrange functional (13) over Lagrange coefficients λ [5,17]. The saddle point of this process gives the desired solution.…”

“…Unfortunately, there are no universal methods to solve the considered here nonlinear ill-posed problems. Nevertheless, some algorithm based on especial schemes of measurements, suitable approximations, and new achievements in mathematical theory have been worked out and used in this new area [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Dual regularization in inverse problem of low frequency dielectric profiling

“…In this paper, we propose to use in this problem the new approach of dual regularization [4,5] that can be applied to initial differential equations (Maxwell's equations) that gives a possibility to obtain the solution of an inverse problem beyond the range of applicability of the perturbation theory.…”

One-dimensional inverse scattering problem

“…Results of the numerical study [7] for low-frequency conductivity sounding have demonstrated serious limitations of such approach for large perturbations, when the Born approximation (first guess of iterative method) is inapplicable. To overcome these restrictions of perturbation theory, the new method of dual regularization based on the Lagrange approach in the optimization theory [8] has been applied in this problem to solve initial Maxwell equations [9]. Results show its ability to retrieve very strong variations of conductivity profiles.…”

“…In the considered problem it is necessary to use the modified Lagrange function [8]. It can be built as…”