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All-pairs similarity problem asks to find all vector pairs in a set of vectors the similarities of which surpass a given similarity threshold, and it is a computational kernel in data mining and information retrieval for several tasks. We…
Most methods for Bundle Adjustment (BA) in computer vision are either centralized or operate incrementally. This leads to poor scaling and affects the quality of solution as the number of images grows in large scale structure from motion…
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and…
Magnetic Resonance Imaging (MRI) is a kind of medical imaging technology used for diagnostic imaging of diseases, but its image quality may be suffered by the long acquisition time. The compressive sensing (CS) based strategy may decrease…
We define the space of functions of bounded variation ($BV$) on the graph. Using the notion of divergence of flows on graphs, we show that the unit ball of the dual space to $BV$ in the graph setting can be described as the image of the…
In this paper, we study a class of non-convex optimization problems known as multi-affine quadratic equality constrained problems, which appear in various applications--from generating feasible force trajectories in robotic locomotion and…
We propose a new asynchronous parallel block-descent algorithmic framework for the minimization of the sum of a smooth nonconvex function and a nonsmooth convex one, subject to both convex and nonconvex constraints. The proposed framework…
Concerning huge-scale aggregative convex programming of a linear objective subject to the affine constraints of equality and inequality and the quadratic constraints of inequality, convex and aggregatively computable, an algorithm is…
We consider the total variation (TV) minimization problem used for compressive sensing and solve it using the generalized alternating projection (GAP) algorithm. Extensive results demonstrate the high performance of proposed algorithm on…
In this paper, we present a semi-proximal alternating direction method of multipliers (ADMM) for solving $3$-block separable convex minimization problems with the second block in the objective being a strongly convex function and one…
The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…
Abstract Objective. Cone-beam computed tomography is becoming more and more popular in applications such as 3D dental imaging. Iterative methods compared to the standard Feldkamp algorithm have shown improvements in image quality of…
We present an Alternating Direction Method of Multipliers (ADMM) algorithm for solving optimization problems with an l_1 regularized least-squares cost function subject to recursive equality constraints. The considered optimization problem…
To solve the separable convex optimization problem with linear constraints, Eckstein and Bertsekas introduced the generalized alternating direction method of multipliers (in short, GADMM), which is an efficient and simple acceleration…
Parallel imaging has been an essential technique to accelerate MR imaging. Nevertheless, the acceleration rate is still limited due to the ill-condition and challenges associated with the undersampled reconstruction. In this paper, we…
We consider the convex minimization model with both linear equality and inequality constraints, and reshape the classic augmented Lagrangian method (ALM) by balancing its subproblems. As a result, one of its subproblems decouples the…
Electrical capacitance tomography (ECT) has been investigated in many fields due to its advantages of being non-invasive and low cost. Sparse algorithms with l1-norm regularization are used to reduce the smoothing effect and obtain sharp…
We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of…
This paper introduces a dual-regularized ADMM approach to distributed, time-varying optimization. The proposed algorithm is designed in a prediction-correction framework, in which the computing nodes predict the future local costs based on…
In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in [Bai, et al. Generalized symmetric ADMM for separable convex optimization. Comput. Optim. Appl. 70, 129-170 (2018)], as well as its linear…