Related papers: Morozov's principle for the augmented Lagrangian m…

The linearized Bregman iterations (LBreI) and its variants have received considerable attention in signal/image processing and compressed sensing. Recently, LBreI has been extended to a larger class of nonconvex functions, along with…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

We investigate Tikhonov regularization methods for nonlinear ill-posed problems in Banach spaces, where the penalty term is described by Bregman distances. We prove convergence and stability results. Moreover, using appropriate source…

In convex optimization, there is an {\em acceleration} phenomenon in which we can boost the convergence rate of certain gradient-based algorithms. We can observe this phenomenon in Nesterov's accelerated gradient descent, accelerated mirror…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…

We analyze the convergence properties of the consensus-alternating direction method of multipliers (ADMM) for solving general quadratically constrained quadratic programs. We prove that the augmented Lagrangian function value is…

In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…

The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…

We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and…

We consider the problem of minimizing the sum of a smooth function and a composition of a zero-one loss function with a linear operator, namely zero-one composite optimization problem (0/1-COP). It is a versatile model including the support…

We develop a decomposition method based on the augmented Lagrangian framework to solve a broad family of semidefinite programming problems, possibly with nonlinear objective functions, nonsmooth regularization, and general linear…

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

In this paper, we denoise a given noisy image by minimizing a smoothness promoting function over a set of local similarity measures which compare the mean of the given image and some candidate image on a large collection of subboxes. The…

Considering a general linear ill-posed equation, we explore the duality arising from the requirement that the discrepancy should take a given value based on the estimation of the noise level, as is notably the case when using the Morozov…

We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…

Inverse problems arise in a number of domains such as medical imaging, remote sensing, and many more, relying on the use of advanced signal and image processing approaches -- such as sparsity-driven techniques -- to determine their…

In this paper, we establish an initial theory regarding the Second Order Asymptotical Regularization (SOAR) method for the stable approximate solution of ill-posed linear operator equations in Hilbert spaces, which are models for linear…

The convergence rates results in $\ell^1$-regularization when the sparsity assumption is narrowly missed, presented by Burger et al. (2013 Inverse Problems 29 025013), are based on a crucial condition which requires that all basis elements…

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…