相关论文: HPR-LP: An implementation of an HPR method for sol…

This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…

In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…

Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…

Positive linear programs (LPs) model many graph and operations research problems. One can solve for a $(1+\epsilon)$-approximation for positive LPs, for any selected $\epsilon$, in polylogarithmic depth and near-linear work via variations…

The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…

Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of…

Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within…

Linear programming (LP) is an extremely useful tool which has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…

We propose a CPU-GPU heterogeneous computing method for solving time-evolution partial differential equation problems many times with guaranteed accuracy, in short time-to-solution and low energy-to-solution. On a single-GH200 node, the…

Hypercomplex signal processing (HSP) provides state-of-the-art tools to handle multidimensional signals by harnessing intrinsic correlation of the signal dimensions through Clifford algebra. Recently, the hypercomplex representation of the…

Scientific applications produce vast amounts of data, posing grand challenges in the underlying data management and analytic tasks. Progressive compression is a promising way to address this problem, as it allows for on-demand data…

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives…

Linear programming (LP) relaxations are widely employed in exact solution methods for multilinear programs (MLP). One example is the family of Recursive McCormick Linearization (RML) strategies, where bilinear products are substituted for…

In the development of industrial digital twins, the optimization problem of technological and business processes often arises. In many cases, this problem can be reduced to a large-scale linear programming (LP) problem. The article is…

Scaling hyperparameter optimisation to very large datasets remains an open problem in the Gaussian process community. This paper focuses on iterative methods, which use linear system solvers, like conjugate gradients, alternating…

There is a recent interest on first-order methods for linear programming (LP). In this paper,we propose a stochastic algorithm using variance reduction and restarts for solving sharp primal-dual problems such as LP. We show that the…

Symmetric linear solves are fundamental to a wide range of scientific and engineering applications, from climate modeling and structural analysis to machine learning and optimization. These workloads often rely on Cholesky (POTRF)…

Gaussian processes (GPs) are a widely used regression tool, but the cubic complexity of exact solvers limits their scalability. To address this challenge, we extend the GPRat library by incorporating a fully GPU-resident GP prediction…

The simplex algorithm has been successfully used for many years in solving linear programming (LP) problems. Due to the intensive computations required (especially for the solution of large LP problems), parallel approaches have also…

Approximate linear programming (ALP) and its variants have been widely applied to Markov Decision Processes (MDPs) with a large number of states. A serious limitation of ALP is that it has an intractable number of constraints, as a result…