相关论文: A Block Coordinate Descent Method for Sensor Netwo…

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By…

For three decades, carrier-phase observations have been used to obtain the most accurate location estimates using global navigation satellite systems (GNSS). These estimates are computed by minimizing a nonlinear mixed-integer least-squares…

We investigate a class of general combinatorial graph problems, including MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints and solved via the alternating direction method of multipliers…

A common method for delineating urban and suburban boundaries is to identify clusters of spatial units that are highly interconnected in a network of commuting flows, each cluster signaling a cohesive economic submarket. It is critical that…

We propose a bilinear decomposition for the Burer-Monteiro method and combine it with the standard Alternating Direction Method of Multipliers algorithm for semidefinite programming. Bilinear decomposition reduces the degree of the…

This paper studies the subspace clustering problem. Given some data points approximately drawn from a union of subspaces, the goal is to group these data points into their underlying subspaces. Many subspace clustering methods have been…

Deep learning models have become state of the art for natural language processing (NLP) tasks, however deploying these models in production system poses significant memory constraints. Existing compression methods are either lossy or…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…

We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard…

Semidefinite programs (SDPs) and their solvers are powerful tools with many applications in machine learning and data science. Designing scalable SDP solvers is challenging because by standard the positive semidefinite decision variable is…

We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or…

This paper introduces an efficient algorithm for computing the best approximation of a given matrix onto the intersection of linear equalities, inequalities and the doubly nonnegative cone (the cone of all positive semidefinite matrices…

At each iteration of a Block Coordinate Descent method one minimizes an approximation of the objective function with respect to a generally small set of variables subject to constraints in which these variables are involved. The…

Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…

Advancements in information technology have enabled the creation of massive spatial datasets, driving the need for scalable and efficient computational methodologies. While offering viable solutions, centralized frameworks are limited by…

This paper studies the relationship between the nuclear norm-regularized minimization problem, which minimizes the sum of a $C^2$ function $h$ and a positive multiple of the nuclear norm, denoted by $f$, and its factorized problem obtained…

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…

In this paper we analyze a family of general random block coordinate descent methods for the minimization of $\ell_0$ regularized optimization problems, i.e. the objective function is composed of a smooth convex function and the $\ell_0$…