Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1098-1105
The purpose of this paper is to investigate the Tikhonov regularization method for solving a system of ill-posed equilibrium problems in Banach spaces with a posteriori regularization-parameter choice. An application to convex minimization problems with coupled constraints is also given.
Regularization inertial proximal point algorithm for unconstrained vector convex optimization problems
Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1275–1281
The purpose of this paper is to investigate an iterative regularization method of proximal point type for solving ill posed vector convex optimization problems in Hilbert spaces. Applications to the convex feasibility problems and the problem of common fixed points for nonexpansive potential mappings are also given.
Newton-Kantorovich Iterative Regularization for Nonlinear Ill-Posed Equations Involving Accretive Operators
Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 271–276
The Newton-Kantorovich iterative regularization for nonlinear ill-posed equations involving monotone operators in Hilbert spaces is developed for the case of accretive operators in Banach spaces. An estimate for the convergence rates of the method is established.
Ukr. Mat. Zh. - 2003. - 55, № 7. - pp. 991-997
The convergence rates of the regularized solution as well as its Galerkin approximations for nonlinear monotone ill-posed problems in a Banach space are established on the basis of the choice of a regularization parameter by the Morozov discrepancy principle.
Ukr. Mat. Zh. - 2000. - 52, № 2. - pp. 249-256
Convergence rates are justified for regularized solutions of a Hammerstein operator equation of the form x + F 2 F 1(x) = f in the Banach space with monotone perturbations f 2 h and f 1 h .
Convergence rates and finite-dimensional approximation for a class of ill-posed variational inequalities
Ukr. Mat. Zh. - 1997. - 49, № 5. - pp. 629–637
The purpose of this paper is to investigate an operator version of Tikhonov regularization for a class of ill-posed variational inequalities under arbitrary perturbation operators. Aspects of convergence rate and finite-dimensional approximations are considered. An example in the theory of generalized eigenvectors is given for illustration.
The regularization of variational inequalities and a general approximation scheme for regularized solutions in Banach spaces
Ukr. Mat. Zh. - 1991. - 43, № 9. - pp. 1273–1276
Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 539–541
Ukr. Mat. Zh. - 1985. - 37, № 2. - pp. 186 – 191