Related papers: Efficient coordinate-descent for orthogonal matric…

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by rank-1 matrices, the matrices can be obtained…

This paper exploits a basic connection between sequential quadratic programming and Riemannian gradient optimization to address the general question of selecting a metric in Riemannian optimization, in particular when the Riemannian…

QR decomposition is used prevalently in wireless communication. In this paper, we express the Givens-rotation-based QR decomposition algorithm on a spatial architecture using T2S (Temporal To Spatial), a high-productivity spatial…

In this paper an approach for finding a sparse incomplete Cholesky factor through an incomplete orthogonal factorization with Givens rotations is discussed and applied to Gaussian Markov random fields (GMRFs). The incomplete Cholesky factor…

In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…

Composite convex optimization models arise in several applications, and are especially prevalent in inverse problems with a sparsity inducing norm and in general convex optimization with simple constraints. The most widely used algorithms…

This paper addresses the problem of finding the closest generalized essential matrix from a given $6\times 6$ matrix, with respect to the Frobenius norm. To the best of our knowledge, this nonlinear constrained optimization problem has not…

Training and inference in Gaussian processes (GPs) require solving linear systems with $n\times n$ kernel matrices. To address the prohibitive $\mathcal{O}(n^3)$ time complexity, recent work has employed fast iterative methods, like…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

Convolution is one of the fundamental operations of deep neural networks with demanding matrix computation. In a graphic processing unit (GPU), Tensor Core is a specialized matrix processing hardware equipped with reduced-precision…

Neuroscientists fit morphologically and biophysically detailed neuron simulations to physiological data, often using evolutionary algorithms. However, such gradient-free approaches are computationally expensive, making convergence slow when…

Variational formulations of reconstruction in computed tomography have the notable drawback of requiring repeated evaluations of both the forward Radon transform and either its adjoint or an approximate inverse transform which are…

We consider the problem of minimizing a non-convex function over a smooth manifold $\mathcal{M}$. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM) which only requires computing a projection onto a…

This paper presents a new algorithm for generating planar circle patterns. The algorithm employs gradient descent and conjugate gradient method to compute circle radii and centers separately. Compared with existing algorithms, the proposed…

Sparse principal component analysis (PCA), an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the nonsmooth Riemannian optimization problem associated with the…

Many modern machine learning algorithms such as generative adversarial networks (GANs) and adversarial training can be formulated as minimax optimization. Gradient descent ascent (GDA) is the most commonly used algorithm due to its…

The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…

Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…

In the paper, we propose solving optimization problems (OPs) and understanding the Newton method from the optimal control view. We propose a new optimization algorithm based on the optimal control problem (OCP). The algorithm features…

This paper introduces several new algorithms for consensus over the special orthogonal group. By relying on a convex relaxation of the space of rotation matrices, consensus over rotation elements is reduced to solving a convex problem with…