Related papers: Regularization Methods for Ill-Posed Problems in M…
We propose a general framework of iteratively reweighted l1 methods for solving lp regularization problems. We prove that after some iteration k, the iterates generated by the proposed methods have the same support and sign as the limit…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…
We prove the two-scale transformation method which allows rigorous homogenisation of problems defined on locally periodic domains by transformation on periodic domains. The idea to consider periodic substitute problems was originally…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…
A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the…
From the viewpoint of inverse problem, the optimization of drug release based on the multi-laminated drug controlled release devices has been regarded as the solution problem of the diffusion equation initial value inverse problem. In view…
The problem of robustly, asymptotically stabilizing a point (or a set) with two output-feedback hybrid controllers is considered. These control laws may have different objectives, e.g., the closed-loop systems resulting with each controller…
Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates ${u_n}$ converges weakly to a point in the…
We study a class of bilevel convex optimization problems where the goal is to find the minimizer of an objective function in the upper level, among the set of all optimal solutions of an optimization problem in the lower level. A wide range…
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…
We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of…
Mixup is a data augmentation technique that creates new examples as convex combinations of training points and labels. This simple technique has empirically shown to improve the accuracy of many state-of-the-art models in different settings…
Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
Accurate and reliable probability predictions are essential for multi-class supervised learning tasks, where well-calibrated models enable rational decision-making. While isotonic regression has proven effective for binary calibration, its…
Multiscale models allow for the treatment of complex phenomena involving different scales, such as remodeling and growth of tissues, muscular activation, and cardiac electrophysiology. Numerous numerical approaches have been developed to…
Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting, we…
A new formalism to express and operate on diversity measures of qualitative variables, built in a Hilbert space, is presented. The abstract character of the Hilbert space naturally incorporates the equivalence between qualitative variables…
Two methods of level set type are proposed for solving the Cauchy problem for an elliptic equation. Convergence and stability results for both methods are proven, characterizing the iterative methods as regularization methods for this…