相关论文: Sparse preconditioning for model predictive contro…

We present an approach for accelerating nonlinear model predictive control. If the current optimal input signal is saturated, also the optimal signals in subsequent time steps often are. We propose to use the open-loop optimal input signals…

Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we…

This paper presents fast solvers for linear systems arising from the discretization of fractional nonlinear Schr\"odinger equations with Riesz derivatives and attractive nonlinearities. These systems are characterized by complex symmetry,…

At the heart of Newton based optimization methods is a sequence of symmetric linear systems. Each consecutive system in this sequence is similar to the next, so solving them separately is a waste of computational effort. Here we describe…

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the…

The authors propose a recycling Krylov subspace method for the solution of a sequence of self-adjoint linear systems. Such problems appear, for example, in the Newton process for solving nonlinear equations. Ritz vectors are automatically…

In this work, we propose a generalized alternating nonlinear generalized minimal residual method (GA-NGMRES) to accelerate first-order optimization schemes for PDE-constrained optimization problems governed by transport equations. We apply…

We propose an efficient framework for amortized conditional inference by leveraging exact conditional score-guided diffusion models to train a non-reversible neural network as a conditional generative model. Traditional normalizing flow…

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…

In this note we present a multigrid preconditioning method for solving quadratic optimization problems constrained by a fractional diffusion equation. Multigrid methods within the all-at-once approach to solve the first order-order…

The modular open-source framework GRAMPC-D for model predictive control of distributed systems is presented in this paper. The modular concept allows to solve optimal control problems (OCP) in a centralized and distributed fashion using the…

Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this…

We introduce a numerical solver for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. To solve the nonlinear system on each grid cell derived from the SGS method, a fixed-point iteration preconditioned…

Pre-conditioning is a well-known concept that can significantly improve the convergence of optimization algorithms. For noise-free problems, where good pre-conditioners are not known a priori, iterative linear algebra methods offer one way…

We propose using greedy and randomized Kaczmarz inner-iterations as preconditioners for the right-preconditioned flexible GMRES method to solve consistent linear systems, with a parameter tuning strategy for adjusting the number of inner…

In this paper, we consider estimating sparse inverse covariance of a Gaussian graphical model whose conditional independence is assumed to be partially known. Similarly as in [5], we formulate it as an $l_1$-norm penalized maximum…

Synthetic control methods often rely on matching pre-treatment characteristics (called predictors) of the treated unit. The choice of predictors and how they are weighted plays a key role in the performance and interpretability of synthetic…

In this article, the focus is mainly on gaining the optimal control for the unstable power system models and stabilizing them through the Riccati-based feedback stabilization process with sparsity-preserving techniques. We are to find the…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver…