相关论文: R-Continuity with Applications to Convergence Anal…

We consider Tikhonov-type variational regularization of ill-posed linear operator equations in Banach spaces with general convex penalty functionals. Upper bounds for certain error measures expressing the distance between exact and…

We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…

Tensor ring (TR) decomposition has been successfully used to obtain the state-of-the-art performance in the visual data completion problem. However, the existing TR-based completion methods are severely non-convex and computationally…

Convex optimization recently emerges as a compelling framework for performing super resolution, garnering significant attention from multiple communities spanning signal processing, applied mathematics, and optimization. This article offers…

We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…

In this article, we set up the continuous maximal regularity theory for a class of linear differential operators on manifolds with singularities. These operators exhibit degenerate or singular behaviors while approaching the singular ends.…

We consider variational regularization of nonlinear inverse problems in Banach spaces using Tikhonov functionals. This article addresses the problem of $\Gamma$-convergence of a family of Tikhonov functionals and assertions of the…

Contrast variation small-angle neutron scattering (CV-SANS) has been widely employed for nano structural analysis of multicomponent systems. In CV-SANS experiments, scattering intensities of samples with different scattering co\ ntrasts are…

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.…

Most of the literature on the solution of linear ill-posed operator equations, or their discretization, focuses only on the infinite-dimensional setting or only on the solution of the algebraic linear system of equations obtained by…

We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone…

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…

Further studies on the corner singularity of GS reconstruction are are compiled in this paper. It's focused on solution of the Data Completion (DC) problem with the Extended Hilbert Transform (EHT) over plane rectangular region. Optimal…

We focus on the linear convergence of generalized proximal point algorithms for solving monotone inclusion problems. Under the assumption that the associated monotone operator is metrically subregular or that the inverse of the monotone…

An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…

We study the inverse conductivity problem with discontinuous conductivities. We consider, simultaneously, a regularisation and a discretisation for a variational approach to solve the inverse problem. We show that, under suitable choices of…

The circuit-theoretic origins of maximal monotonicity are revisited using modern optimization algorithms for maximal monotone operators. We present an algorithm for computing the periodic behavior of an interconnection of maximal monotone…

This paper presents a decentralized algorithm for a team of agents to track time-varying fixed points that are the solutions to time-varying convex optimization problems. The algorithm is first-order, and it allows for total asynchrony in…

In this paper we prove and discuss some new $\left( H_{p},weak-L_{p}\right) $ type inequalities of maximal operators of $T$ means with respect to Vilenkin systems with monotone coefficients. We also apply these results to prove a.e.…

We consider resolvent splitting algorithms for finding a zero of the sum of finitely many maximally monotone operators. The standard approach to solving this type of problem involves reformulating as a two-operator problem in the…