Related papers: Structured preconditioning of conjugate gradients …
Model Predictive Control (MPC) is a versatile approach capable of accommodating diverse control requirements that holds significant promise for a broad spectrum of industrial applications. Noteworthy challenges associated with MPC include…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
We present a distributed conjugate gradient method for distributed optimization problems, where each agent computes an optimal solution of the problem locally without any central computation or coordination, while communicating with its…
Off-lattice agent-based models (or cell-based models) of multicellular systems are increasingly used to create in-silico models of in-vitro and in-vivo experimental setups of cells and tissues, such as cancer spheroids, neural crest cell…
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…
Solving systems of linear equations is a problem occuring frequently in water engineering applications. Usually the size of the problem is too large to be solved via direct factorization. One can resort to iterative approaches, in…
We consider stochastic approximations which arise from such applications as data communications and image processing. We demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be…
Solving large-scale linear systems problems is a cornerstone in scientific and industrial computing. Classical iterative solvers face increasing difficulty as the number of unknowns becomes large, while fully quantum linear solvers require…
We introduce a new preconditioner for a recently developed pressure-robust hybridized discontinuous Galerkin (HDG) finite element discretization of the Stokes equations. A feature of HDG methods is the straightforward elimination of…
The focus of this work is on the construction and analysis of optimal-order multigrid preconditioners to be used in the Newton-Krylov method for a distributed optimal control problem constrained by the stationary Navier-Stokes equations. As…
We revisit gradient-based optimization for infinite projected entangled pair states (iPEPS), a tensor network ansatz for simulating many-body quantum systems. This approach is hindered by two major challenges: the high computational cost of…
We propose an adaptive mixed precision and dynamically scaled preconditioned conjugate gradient algorithm (AMP-PCG). It dynamically adjusts the precision for storing vectors and computing, exploiting low precision when appropriate, while…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
Linear solvers are key components in any software platform for scientific and engineering computing. The solution of large and sparse linear systems lies at the core of physics-driven numerical simulations relying on partial differential…
Numerical simulation of fracture contact poromechanics is essential for various applications, including CO2 sequestration, geothermal energy production and underground gas storage. Modeling this problem accurately presents significant…
Alternating least squares (ALS) is often considered the workhorse algorithm for computing the rank-R canonical tensor approximation, but for certain problems its convergence can be very slow. The nonlinear conjugate gradient (NCG) method…
Properties of Superiorized Preconditioned Conjugate Gradient (SupPCG) algorithms in image reconstruction from projections are examined. Least squares (LS) is usually chosen for measuring data-inconsistency in these inverse problems.…
This paper presents a case study of application of the preconditioned method of conjugate gradients (CG) on a problem with operator resembling the structure of sum of Kronecker products. In particular, we are solving the Poisson's equation…
In this paper we propose an efficiently preconditioned Newton method for the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices. A sequence of preconditioners based on the BFGS update formula is…
In this paper we consider optimal control of nonlinear time-dependent fluid structure interactions. To determine a time-dependent control variable a BFGS algorithm is used, whereby gradient information is computed via a dual problem. To…