An iterative approach to a constrained least squares problem.
An optimal order yielding discrepancy principle for simplified regularization of ill-posed problems in Hilbert scales.
Approximating curve and strong convergence of the algorithm for the split feasibility problem.
Arcangeli's type discrepancy principles for a class of regularization methods using a modified projection scheme.
Continuous dependence of solutions for ill-posed evolution problems.
Convergence rates for regularization with sparsity constraints.
Dynamical systems method for solving linear finite-rank operator equations
A version of the dynamical systems method (DSM) for solving ill-conditioned linear algebraic systems is studied. An a priori and an a posteriori stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.
Dynamical systems method for solving linear ill-posed problems
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning the discrepancy principle for choosing the regularization parameter are obtained.
Employing different loss functions for the classification of images via supervised learning
Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions....
Ill-posed equations with transformed argument.
Inverse problems in spaces of measures
The ill-posed problem of solving linear equations in the space of vector-valued finite Radon measures with Hilbert space data is considered. Approximate solutions are obtained by minimizing the Tikhonov functional with a total variation penalty. The well-posedness of this regularization method and further regularization properties are mentioned. Furthermore, a flexible numerical minimization algorithm is proposed which converges subsequentially in the weak* sense and with rate 𝒪(n-1)...
Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations
We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is with , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator. The parameter...
On Morozov's method for Tikhonov regularization as an optimal order yielding algorithm.
Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations.
Optimal regularization method for ill-posed Cauchy problems.
Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition.
Quasireversibility for inhomogeneous ill-posed problems in Hilbert spaces.
Regularization for evolution equations in Hilbert spaces involving monotone operators via the semi-flows method.
Representations for the Drazin inverse of bounded operators on Banach space.
Solvability of boundary value problems for operator-differential equations of mixed type.