Related papers: A Nonlinear Acceleration Method for Iterative Algo…
Adaptive thresholding methods have proved to yield high SNRs and fast convergence in finding the solution to the Compressed Sensing (CS) problems. Recently, it was observed that the robustness of a class of iterative sparse recovery…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
Nonlinear acceleration algorithms improve the performance of iterative methods, such as gradient descent, using the information contained in past iterates. However, their efficiency is still not entirely understood even in the quadratic…
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the original direct sampling method (DSM) by incorporating an…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…
This work proposes a novel adaptive linearized alternating direction multiplier method (LADMM) to convex optimization, which improves the convergence rate of the LADMM-based algorithm by adjusting step-size iteratively.The innovation of…
In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional forms and associated parameters of…
We develop a novel iterative direct sampling method (IDSM) for solving linear or nonlinear elliptic inverse problems with partial Cauchy data. It integrates three innovations: a data completion scheme to reconstruct missing boundary…
In this paper, we consider nonconvex optimization problems with nonsmooth nonconvex objective function and nonlinear equality constraints. We assume that both the objective function and the functional constraints can be separated into 2…
Incremental methods are widely utilized for solving finite-sum optimization problems in machine learning and signal processing. In this paper, we study a family of incremental methods -- including incremental subgradient, incremental…
In this paper, we introduce an iterative numerical method to solve systems of nonlinear equations. The third-order convergence of this method is analyzed. Several examples are given to illustrate the efficiency of the proposed method.
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…
In this paper, we propose an inertial alternating direction method of multipliers for solving a class of non-convex multi-block optimization problems with \emph{nonlinear coupling constraints}. Distinctive features of our proposed method,…
We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the…