相关论文: Optimal Polynomial Smoothers for Parallel AMG

We describe a parallel approximation algorithm for maximizing monotone submodular functions subject to hereditary constraints on distributed memory multiprocessors. Our work is motivated by the need to solve submodular optimization problems…

This research introduce our work on developing Krylov subspace and AMG solvers on NVIDIA GPUs. As SpMV is a crucial part for these iterative methods, SpMV algorithms for single GPU and multiple GPUs are implemented. A HEC matrix format and…

We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may…

Pose graph optimization (PGO) is fundamental to robot perception and navigation systems, serving as the mathematical backbone for solving simultaneous localization and mapping (SLAM). Existing solvers suffer from polynomial growth in…

Dedicated hardware accelerators are suitable for parallel computational tasks. Moreover, they have the tendency to accept inexact results. These hardware accelerators are extensively used in image processing and computer vision…

We introduce a unified framework for computing approximately-optimal preconditioners for solving linear and non-linear systems of equations. We demonstrate that the condition number minimization problem, under structured transformations…

Polynomial preconditioning can improve the convergence of the Arnoldi method for computing eigenvalues. Such preconditioning significantly reduces the cost of orthogonalization; for difficult problems, it can also reduce the number of…

We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…

We solve the following problem: given a polynomial of order $n$ and the corresponding $B\'ezier$ tensor product patches over an unstructured regular quadrilateral mesh of any valence, find a solution to the $G^{1}1$ or $C^{1}1$…

The Potts model has many applications. It is equivalent to some min-cut and max-flow models. Primal-dual algorithms have been used to solve these problems. Due to the special structure of the models, convergence proof is still a difficult…

The introduction of accelerator devices such as graphics processing units (GPUs) has had profound impact on molecular dynamics simulations and has enabled order-of-magnitude performance advances using commodity hardware. To fully reap these…

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the…

Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…

We investigate the problem of certifying optimality for sparse generalized linear models (GLMs), where sparsity is enforced through a cardinality constraint. While Branch-and-Bound (BnB) frameworks can certify optimality using perspective…

Topology optimization for large scale problems continues to be a computational challenge. Several works exist in the literature to address this topic, and all make use of iterative solvers to handle the linear system arising from the Finite…

We propose a globally-accelerated, first-order method for the optimization of smooth and (strongly or not) geodesically-convex functions in a wide class of Hadamard manifolds. We achieve the same convergence rates as Nesterov's accelerated…

In this paper, we aim to provide a comprehensive analysis on the linear rate convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex composite optimization problems. Under a certain…

This paper investigates the collision-free control problem for multi-agent systems. For such multi-agent systems, it is the typical situation where conventional methods using either the usual centralized model predictive control (MPC), or…

GPUs have significantly accelerated first-order methods for large-scale optimization, especially in continuous optimization. However, this success has not transferred cleanly to problems with discrete variables, combinatorial structure, and…