Related papers: Backing PDHG into a Corner

The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…

In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…

The geometric multigrid method (GMG) is one of the most efficient solving techniques for discrete algebraic systems arising from elliptic partial differential equations. GMG utilizes a hierarchy of grids or discretizations and reduces the…

This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…

Iterative algorithms with feedback are amongst the most powerful and versatile optimization methods for phase retrieval. Among these, the hybrid input-output algorithm has demonstrated practical solutions to giga-element nonlinear phase…

Differentiable model predictive control (MPC) offers a powerful framework for combining learning and control. However, its adoption has been limited by the inherently sequential nature of traditional optimization algorithms, which are…

In the FPGA (Field Programmable Gate Arrays) design flow, one of the most time-consuming step is the routing of nets. Therefore, there is a need to accelerate it. In a recent paper by Hoo et. al., the authors have developed a Linear…

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

Matrix multiplication is a foundational operation in scientific computing and machine learning, yet its computational complexity makes it a significant bottleneck for large-scale applications. The shift to parallel architectures, primarily…

This paper proposes a combination of a hybrid CPU--GPU and a pure GPU software implementation of a direct algorithm for solving shifted linear systems $(A - \sigma I)X = B$ with large number of complex shifts $\sigma$ and multiple…

We introduce two novel primal-dual algorithms for addressing nonconvex, nonconcave, and nonsmooth saddle point problems characterized by the weak Minty Variational Inequality (MVI). The first algorithm, Nonconvex-Nonconcave Primal-Dual…

The trade-off between pull-based and push-based graph processing engines is well-understood. On one hand, pull-based engines can achieve higher throughput because their workloads are read-dominant, rather than write-dominant, and can…

In the next decade, the demands for computing in large scientific experiments are expected to grow tremendously. During the same time period, CPU performance increases will be limited. At the CERN Large Hadron Collider (LHC), these two…

Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…

We analyze restarted PDHG on totally unimodular linear programs. In particular, we show that restarted PDHG finds an $\epsilon$-optimal solution in $O( H m_1^{2.5} \sqrt{\textbf{nnz}(A)} \log(H m_2 /\epsilon) )$ matrix-vector multiplies…

We present a new parallel algorithm for probabilistic graphical model optimization. The algorithm relies on data-parallel primitives (DPPs), which provide portable performance over hardware architecture. We evaluate results on CPUs and GPUs…

Multi-depot vehicle routing problems (MDVRPs) are prevalent in a variety of practical applications. However, they are computationally challenging to solve due to their inherent complexity. This paper proposes an effective hybrid algorithm…

We propose and analyze an iterative high-order hybridized discontinuous Galerkin (iHDG) discretization for linear partial differential equations. We improve our previous work (SIAM J. Sci. Comput. Vol. 39, No. 5, pp. S782--S808) in several…

This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…

Neural graphics primitives, parameterized by fully connected neural networks, can be costly to train and evaluate. We reduce this cost with a versatile new input encoding that permits the use of a smaller network without sacrificing…