Related papers: An iterative Bregman regularization method for opt…
In this article we investigate an inexact iterative regularization method based on generalized Bregman distances of an optimal control problem with control constraints. We show robustness and convergence of the inexact Bregman method under…
In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and…
In this article we continue our investigation of the iterative regularization method for optimization problems based on Bregman distances. The optimization problems are subject to pointwise inequality constraints in $L^2(\Omega)$. We…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
Regularization and interior point approaches offer valuable perspectives to address constrained nonlinear optimization problems in view of control applications. This paper discusses the interactions between these techniques and proposes an…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
Regularization by the Shannon entropy enables us to efficiently and approximately solve optimal transport problems on a finite set. This paper is concerned with regularized optimal transport problems via Bregman divergence. We introduce the…
This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…
Regularisation theory in Banach spaces, and non--norm-squared regularisation even in finite dimensions, generally relies upon Bregman divergences to replace norm convergence. This is comparable to the extension of first-order optimisation…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained…
We investigate local optimality conditions of first and second order for integer optimal control problems with total variation regularization via a finite-dimensional switching point problem. We show the equivalence of local optimality for…
This work addresses the problem of error concealment in video transmission systems over noisy channels employing Bregman divergences along with regularization. Error concealment intends to improve the effects of disturbances at the…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
We consider Tikhonov regularization of control-constrained optimal control problems. We present new a-priori estimates for the regularization error assuming measure and source-measure conditions. In the special case of bang-bang solutions,…
In this paper we propose optimisation methods for variational regularisation problems based on discretising the inverse scale space flow with discrete gradient methods. Inverse scale space flow generalises gradient flows by incorporating a…
The aim of this paper is to introduce and study a two-step debiasing method for variational regularization. After solving the standard variational problem, the key idea is to add a consecutive debiasing step minimizing the data fidelity on…
Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…
In this paper we develop a Bregman regularized proximal point algorithm for solving monotone equilibrium problems on Hadamard manifolds. It has been shown that the regularization term induced by a Bregman function is, in general, nonconvex…