Related papers: Stochastic convergence of regularized solutions fo…
We consider joint Tikhonov- and Lavrentiev-regularization of control problems with pointwise control- and state-constraints. We derive error estimates for the error which is introduced by the Tikhonov regularization. With the help of this…
We investigate the strong convergence properties of a proximal-gradient inertial algorithm with two Tikhonov regularization terms in connection to the minimization problem of the sum of a convex lower semi-continuous function $f$ and a…
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…
In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under {\it…
In this paper, we develop an optimization-based framework for solving coupled forward-backward stochastic differential equations. We introduce an integral-form objective function and prove its equivalence to the error between consecutive…
This paper is concerned with the introduction of Tikhonov regularization into least squares approximation scheme on $[-1,1]$ by orthonormal polynomials, in order to handle noisy data. This scheme includes interpolation and…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
This paper deals with a second order dynamical system with a Tikhonov regularization term in connection to the minimization problem of a convex Fr\'echet differentiable function. The fact that beside the asymptotically vanishing damping we…
In this contribution we show sufficient conditions for simultaneous unique identification of unknown spacewise coefficients and heat source in a parabolic partial differential equation given additional final time measurements. Our approach…
In this article, we investigate both forward and backward problems for coupled systems of time-fractional diffusion equations, encompassing scenarios of strong coupling. For the forward problem, we establish the well-posedness of the…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
Stochastic gradient descent is one of the most successful approaches for solving large-scale problems, especially in machine learning and statistics. At each iteration, it employs an unbiased estimator of the full gradient computed from one…
In this paper we consider the computation of approximate solutions for inverse problems in Hilbert spaces. In order to capture the special feature of solutions, non-smooth convex functions are introduced as penalty terms. By exploiting the…
This paper explores the incorporation of Tikhonov regularization into the least squares approximation scheme using trigonometric polynomials on the unit circle. This approach encompasses interpolation and hyperinterpolation as specific…
Solving equilibrium problems under constraints is an important problem in optimization and optimal control. In this context an important practical challenge is the efficient incorporation of constraints. We develop a continuous-time method…
Fractional Tikhonov regularization methods have been recently proposed to reduce the oversmoothing property of the Tikhonov regularization in standard form, in order to preserve the details of the approximated solution. Their regularization…
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…
In this work, an accurate regularization technique based on the Meyer wavelet method is developed to solve the ill-posed backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". In principle,…
This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex…