Related papers: Tikhonov regularization of control-constrained opt…
In this work, we investigate the optimal control problem for continuous-time Markov decision processes with the random impact of the environment. We provide conditions to show the existence of optimal controls under finite-horizon criteria.…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…
This paper addresses Tikhonov like regularization methods with convex penalty functionals for solving nonlinear ill-posed operator equations formulated in Banach or, more general, topological spaces. We present an approach for proving…
This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on $B^0_{p,1}$ penalty terms which yield estimators that are sparse with respect to a wavelet…
We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study…
A class of stochastic optimal control problems involving optimal stopping is considered. Methods of Krylov are adapted to investigate the numerical solutions of the corresponding normalized Bellman equations and to estimate the rate of…
We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discuss the upper convergence rates of Tikhonov regularizer under…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
We study Tikhonov regularization for solving ill--posed operator equations where the solutions are functions defined on surfaces. One contribution of this paper is an error analysis of Tikhonov regularization which takes into account…
Many applications in science and engineering require the solution of large linear discrete ill-posed problems that are obtained by the discretization of a Fredholm integral equation of the first kind in several space-dimensions. The matrix…
This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
We consider Tikhonov-type variational regularization of ill-posed linear operator equations in Banach spaces with general convex penalty functionals. Upper bounds for certain error measures expressing the distance between exact and…
We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we…
Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary…
We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then…
In this paper, we investigate iterative methods that are based on sampling of the data for computing Tikhonov-regularized solutions. We focus on very large inverse problems where access to the entire data set is not possible all at once…