Related papers: Discretized Tikhonov regularization for Robin boun…

We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates…

In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…

We consider the reconstruction of a heterogeneous coefficient field in a Robin boundary condition on an inaccessible part of the boundary in a Poisson problem with an uncertain (or unknown) inhomogeneous conductivity field in the interior…

We propose a simple boundary condition regularization strategy to reduce error propagation in pressure field reconstruction from corrupted image velocimetry data. The core idea is to replace the canonical Neumann boundary conditions with…

We study parameter identification problems in a structured population model without mutations. Given measurements of the total population size or critical points of the population, we aim to recover its growth rate, death rate or initial…

We consider an elliptic problem with unknowns on the boundary of the domain of the elliptic equation and suppose that the right-hand side of this equation is square integrable and that the boundary data are arbitrary (specifically,…

This paper focuses on the regularization of backward time-fractional diffusion problem on unbounded domain. This problem is well-known to be ill-posed, whence the need of a regularization method in order to recover stable approximate…

In this article, we consider the Tikhonov regularization of an optimal control problem of semilinear partial differential equations with box constraints on the control. We derive a-priori regularization error estimates for the control under…

In this work, first we employ a penalization technique to analyze a Dirichlet boundary feedback control problem pertaining to reaction-diffusion equation. We establish the stabilization result of the equivalent Robin problem in the…

We study second order parabolic equations on Lipschitz domains subject to inhomogeneous Neumann (or, more generally, Robin) boundary conditions. We prove existence and uniqueness of weak solutions and their continuity up to the boundary of…

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to…

We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of…

Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers…

We consider hierarchical variational inequality problems, or more generally, variational inequalities defined over the set of zeros of a monotone operator. This framework includes convex optimization over equilibrium constraints and…

For linear inverse problem with Gaussian random noise we show that Tikhonov regularization algorithm is minimax in the class of linear estimators and is asymptotically minimax in the sense of sharp asymptotic in the class of all estimators.…

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to…

These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…

In this work we consider the stable numerical solution of large-scale ill-posed nonlinear least squares problems with nonzero residual. We propose a non-stationary Tikhonov method with inexact step computation, specially designed for…

In the first part of this article we deal with the existence of at least three non-trivial weak solutions of a nonlocal problem with nonstandard growth involving a nonlocal Robin type boundary condition. The second part of the article is…

In this work, we consider the linear inverse problem $y=Ax+\epsilon$, where $A\colon X\to Y$ is a known linear operator between the separable Hilbert spaces $X$ and $Y$, $x$ is a random variable in $X$ and $\epsilon$ is a zero-mean random…