Related papers: Multigrid for Bundle Adjustment
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
Preconditioning is at the core of modern many-fermion Monte Carlo algorithms, such as Hybrid Monte Carlo, where the repeated solution of a linear problem involving an ill-conditioned matrix is needed. We report on a performance comparison…
In this article we construct and analyze multigrid preconditioners for discretizations of operators of the form D+K* K, where D is the multiplication with a relatively smooth positive function and K is a compact linear operator. These…
Recently, the cross-modal pretraining model has been employed to produce meaningful pseudo-labels to supervise the training of an image clustering model. However, numerous erroneous alignments in a cross-modal pre-training model could…
This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for…
The use of multigrid and related preconditioners with the finite element method is often limited by the difficulty of applying the algorithm effectively to a problem, especially when the domain has a complex shape or adaptive refinement. We…
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…
A cutting-plane model for a nonsmooth function is the maximum of several first-order expansions centered at different points. Using such a model in a bundle method leads to linear convergence (of serious steps) to a minimum. In smooth…
We deal with accelerating the solution of a sequence of large linear systems solved by preconditioned conjugate gradient method (PCG). The sequence originates from time-stepping within a simulation of an unsteady incompressible flow. We…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
In this paper, we study a general optimization model, which covers a large class of existing models for many applications in imaging sciences. To solve the resulting possibly nonconvex, nonsmooth and non-Lipschitz optimization problem, we…
Maintaining instantaneous balance between electricity supply and demand is critical for reliability and grid instability. System operators achieve this through solving the task of Unit Commitment (UC),ca high dimensional large-scale…
This paper studies the fast adaptive beamforming for the multiuser multiple-input single-output downlink. Existing deep learning-based approaches assume that training and testing channels follow the same distribution which causes task…
In this paper, we develop a multigrid method on unstructured shape-regular grids. For a general shape-regular unstructured grid of ${\cal O}(N)$ elements, we present a construction of an auxiliary coarse grid hierarchy on which a geometric…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
Due to the wide separation of time scales in geophysical fluid dynamics, semi-implicit time integrators are commonly used in operational atmospheric forecast models. They guarantee the stable treatment of fast (acoustic and gravity) waves,…
In addition to the best model architecture and hyperparameters, a full AutoML solution requires selecting appropriate hardware automatically. This can be framed as a multi-objective optimization problem: there is not a single best hardware…
Energy and pollution are urging problems of the 21th century. By gradually changing the actual power grid system, smart grid may evolve into different systems by means of size, elements and strategies, but its fundamental requirements and…
We study generalized linear prediction under a streaming setting, where each iteration uses only one fresh data point for a gradient-level update. While momentum is well-established in deterministic optimization, a fundamental open question…
Prompt tuning has become a new paradigm for model tuning and it has demonstrated success in natural language pretraining and even vision pretraining. In this work, we explore the transfer of prompt tuning to multimodal pretraining, with a…