Related papers: Higher order error estimates for regularization of…
We propose a new class of exact continuous relaxations of l0-regularized criteria involving non-quadratic data terms such as the Kullback-Leibler divergence and the logistic regression, possibly combined with an l2 regularization. We first…
This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
We study variational regularization methods in a general framework, more precisely those methods that use a discrepancy and a regularization functional. While several sets of sufficient conditions are known to obtain a regularization…
A novel Follow-the-Perturbed-Leader type algorithm is proposed and analyzed for solving general long-term constrained optimization problems in an online manner, where the target and constraint functions are oblivious adversarially generated…
We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…
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…
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…
In this paper, we consider the inverse source problem for the time-fractional diffusion equation, which has been known to be an ill-posed problem. To deal with the ill-posedness of the problem, we propose to transform the problem into a…
We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation…
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…
We provide estimators for a large class of inverse problems, including nonlinear inverse problems. Using complexity regularization technics we provide adaptive estimators achieving the best rate over the collection of models.
A general deterministic analysis to state the necessary conditions with a coefficient determination for the variational source condition to hold is provided. Of particular interest in terms of the choice of the regularization parameter, it…
We consider the problem of recovering the unknown noise variance in the linear regression model. To estimate the nuisance (a vector of regression coefficients) we use a family of spectral regularisers of the maximum likelihood estimator.…
Stability and error analysis remain challenging for problems that lack regularity properties near solutions, are subject to large perturbations, and might be infinite dimensional. We consider nonconvex optimization and generalized equations…
We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form in H\"older spaces with variable exponent. The procedure allows to…
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…
In this work, we develop a level-set subdifferential error bound condition aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…