相关论文: Deviation Maximization for Rank-Revealing QR Facto…

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on…

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…

Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic.…

The discrete empirical interpolation method (DEIM) may be used as an index selection strategy for formulating a CUR factorization. A notable drawback of the original DEIM algorithm is that the number of column or row indices that can be…

Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…

We present the LU decomposition with panel rank revealing pivoting (LU_PRRP), an LU factorization algorithm based on strong rank revealing QR panel factorization. LU_PRRP is more stable than Gaussian elimination with partial pivoting…

Q-learning is a widely used reinforcement learning technique for solving path planning problems. It primarily involves the interaction between an agent and its environment, enabling the agent to learn an optimal strategy that maximizes…

In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer with suitable proximal parameter to each of the first…

Vector quantization is a fundamental operation for data compression and vector search. To obtain high accuracy, multi-codebook methods represent each vector using codewords across several codebooks. Residual quantization (RQ) is one such…

Reinforcement learning methods typically use Deep Neural Networks to approximate the value functions and policies underlying a Markov Decision Process. Unfortunately, DNN-based RL suffers from a lack of explainability of the resulting…

Gaussian elimination with full pivoting generates a PLUQ matrix decomposition. Depending on the strategy used in the search for pivots, the permutation matrices can reveal some information about the row or the column rank profiles of the…

We introduce a QPLEX Decision Process (QDP) as a model for dynamic control of queueing systems with non-stationary arrivals, general service distributions, and service-level chance constraints. QDPs integrate QPLEX, a computational modeling…

Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant…

The low-rank quaternion matrix approximation has been successfully applied in many applications involving signal processing and color image processing. However, the cost of quaternion models for generating low-rank quaternion matrix…

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

We develop two iterative algorithms for solving the low rank phase retrieval (LRPR) problem. LRPR refers to recovering a low-rank matrix $\X$ from magnitude-only (phaseless) measurements of random linear projections of its columns. Both…

In this work, we consider rank-one adaptations $X_{new} = X+ab^T$ of a given matrix $X\in \mathbb{R}^{n\times p}$ with known matrix factorization $X = UW$, where $U\in\mathbb{R}^{n\times p}$ is column-orthogonal, i.e. $U^TU=I$. Arguably the…

The QR algorithm is one of the three phases in the process of computing the eigenvalues and the eigenvectors of a dense nonsymmetric matrix. This paper describes a task-based QR algorithm for reducing an upper Hessenberg matrix to real…

We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…

When applying eigenvalue decomposition on the quadratic term matrix in a type of linear equally constrained quadratic programming (EQP), there exists a linear mapping to project optimal solutions between the new EQP formulation where $Q$ is…