Related papers: Greedy Block Gauss-Seidel Methods for Solving Larg…
Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent…
Sparsity-constrained optimization has wide applicability in machine learning, statistics, and signal processing problems such as feature selection and compressive Sensing. A vast body of work has studied the sparsity-constrained…
This paper tackles optimal sensor placement for Bayesian linear inverse problems, a popular version of the more general Optimal Experimental Design (OED) problem, using the D-optimality criterion. This is done by establishing connections…
We study a linear quadratic regulation problem with a constraint where the control input can be nonzero only at a limited number of times. Given that this constraint leads to a combinational optimization problem, we adopt a greedy method to…
This paper aims to present a fairly accessible generalization of several symmetric Gauss-Seidel decomposition based multi-block proximal alternating direction methods of multipliers (ADMMs) for convex composite optimization problems. The…
In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like…
Maximum Inner Product Search (MIPS) is an important task in many machine learning applications such as the prediction phase of a low-rank matrix factorization model for a recommender system. There have been some works on how to perform MIPS…
We consider a distributed learning problem in which the computation is carried out on a system consisting of a master node and multiple worker nodes. In such systems, the existence of slow-running machines called stragglers will cause a…
Motivated by the successful use of greedy algorithms for Reduced Basis Methods, a greedy method is proposed that selects N input data in an asymptotically optimal way to solve well-posed operator equations using these N data. The operator…
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an approach based on supervised learning of a greedy…
Communication-avoiding Krylov methods require solving small dense Gram systems at each outer iteration. We present a low-synchronization approach based on Forward Gauss--Seidel (FGS), which exploits the structure of Gram matrices arising…
In the first part of this paper, we prove that, under some natural non-degeneracy assumptions, the Greedy Parabolic Target-Following Method, based on {\em universal tangent direction} has a favorable local behavior. In view of its global…
A grouping-circular-based (GCB) greedy algorithm is proposed to promote the efficiency of mesh deformation. By incorporating the multigrid concept that the computational errors on the fine mesh can be approximated with those on the coarse…
We consider a class of discrete optimization problems that aim to maximize a submodular objective function subject to a distributed partition matroid constraint. More precisely, we consider a networked scenario in which multiple agents…
A new stepsize for gradient method is proposed. Combining it with the exact line search stepsizes, the gradient method achieves the optimal solution in 5 steps for 3 dimensional quadratic function minimization problem. The new stepsize is…
Distributed optimization is pivotal for large-scale signal processing and machine learning, yet communication overhead remains a major bottleneck. Low-rank gradient compression, in which the transmitted gradients are approximated by…
A greedy randomized nonlinear Bregman-Kaczmarz method by sampling the working index with residual information is developed for the solution of the constrained nonlinear system of equations. Theoretical analyses prove the convergence of the…
Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems. Typically these problems are solved numerically using iterative methods. The local minimiserobtained using these iterative…
We address an optimal sensor placement problem through Bayesian experimental design for seismic full waveform inversion for the recovery of the associated moment tensor. The objective is that of optimally choosing the location of the…
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…