相关论文: Factorization of Saddle-point Matrices in Dynamica…

This paper describes the implementation of a new interior point solver for linear programming for the open-source optimization library HiGHS. The solver uses a direct factorisation to solve the Newton systems, choosing the best approach…

This paper introduces a novel framework for matrix diagonalization, recasting it as a sequential decision-making problem and applying the power of Decision Transformers (DTs). Our approach determines optimal pivot selection during…

Matrix factorization (MF) is a widely used collaborative filtering (CF) algorithm for recommendation systems (RSs), due to its high prediction accuracy, great flexibility and high efficiency in big data processing. However, with the…

We consider the problem of computing optimal policies in average-reward Markov decision processes. This classical problem can be formulated as a linear program directly amenable to saddle-point optimization methods, albeit with a number of…

We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…

In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…

A distributed optimal control problem with the constraint of a linear elliptic partial differential equation is considered. A necessary optimality condition for this problem forms a saddle point system, the efficient and accurate solution…

The efficient compression of kernel matrices, for instance the off-diagonal blocks of discretized integral equations, is a crucial step in many algorithms. In this paper, we study the application of Skeletonized Interpolation to construct…

In this paper, we present novel randomized algorithms for solving saddle point problems whose dual feasible region is given by the direct product of many convex sets. Our algorithms can achieve an ${\cal O}(1/N)$ and ${\cal O}(1/N^2)$ rate…

We propose a doubly stochastic primal-dual coordinate optimization algorithm for empirical risk minimization, which can be formulated as a bilinear saddle-point problem. In each iteration, our method randomly samples a block of coordinates…

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered while solving an optimization problem. Standard factorization algorithms are highly efficient but remain…

We present a very fast algorithm for general matrix factorization of a data matrix for use in the statistical analysis of high-dimensional data via latent factors. Such data are prevalent across many application areas and generate an…

Long-time-integrated quantities in stochastic processes, in or out of equilibrium, usually exhibit rare but huge fluctuations. Work or heat production is such a quantity, of which the probability distribution function displays an…

We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal…

The Primal-Dual (PD) algorithm is widely used in convex optimization to determine saddle points. While the stability of the PD algorithm can be easily guaranteed, strict contraction is nontrivial to establish in most cases. This work…

We propose an algorithm to compute the dynamics of articulated rigid-bodies with different sensor distributions. Prior to the on-line computations, the proposed algorithm performs an off-line optimisation step to simplify the computational…

This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform…

We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then propose several structure-exploiting preconditioners to be…

Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…

We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…