相关论文: Adjoint methods for quasisymmetry of vacuum fields…

The adjoint method, recently introduced by Evans, is used to study obstacle problems, weakly coupled systems, cell problems for weakly coupled systems of Hamilton-Jacobi equations, and weakly coupled systems of obstacle type. In particular,…

It is well-known that accelerated gradient first order methods possess optimal complexity estimates for the class of convex smooth minimization problems. In many practical situations, it makes sense to work with inexact gradients. However,…

We study the conjugate gradient method for solving s system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.

We develop a micromorphic-based approach for finite element stabilization of reaction-convection-diffusion equations, by gradient enhancement of the field of interest via introducing an auxiliary variable. The well-posedness of the…

Using a framework based on the $1+3$ formalism we carry out a study on axially and reflection symmetric dissipative fluids, in the quasi--static regime. We first derive a set of invariantly defined "velocities", which allow for an…

In this paper, we present a unified and general framework for analyzing the batch updating approach to nonlinear, high-dimensional optimization. The framework encompasses all the currently used batch updating approaches, and is applicable…

Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…

This Technical Note outlines an adjoint complement to a critical building block of pressure-based Finite-Volume (FV) flow solvers that employ a collocated variable arrangement to simulate virtually incompressible fluids. The focal point is…

Many optimization problems in electrical engineering consider a large number of design parameters. A sensitivity analysis identifies the design parameters with the strongest influence on the problem of interest. This paper introduces the…

Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…

This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This…

This paper presents a majorized alternating direction method of multipliers (ADMM) with indefinite proximal terms for solving linearly constrained $2$-block convex composite optimization problems with each block in the objective being the…

The space of high-beta, approximately quasiaxisymmetric, large-aspect-ratio stellarator configurations is explored using an inverse coordinate approach and a quadratic polynomial ansatz for the flux function, following the method of…

This paper deals with subsampled spectral gradient methods for minimizing finite sum. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods.…

The performance of gradient methods has been considerably improved by the introduction of delayed parameters. After two and a half decades, the revealing of second-order information has recently given rise to the Cauchy-based methods with…

We develop the foundations of the theory of quasi-visual approximations of bounded metric spaces. Roughly speaking, these are sequences of covers of a given space for which the diameters of the sets in the covers shrink to zero and for…

We consider solving nonconvex composite optimization problems in which the sum of a smooth function and a nonsmooth function is minimized. Many of convergence analyses of proximal gradient-type methods rely on global descent property…

Diffractive optical elements with a large diffraction angle require feature sizes down to sub-wavelength dimensions, which require a rigorous electromagnetic computational model for calculation. However, the computational optimization of…

This work aims to numerically construct exactly commuting matrices close to given almost commuting ones, which is equivalent to the joint approximate diagonalization problem. We first prove that almost commuting matrices generically have…

Before a car-following model can be applied in practice, it must first be validated against real data in a process known as calibration. This paper discusses the formulation of calibration as an optimization problem, and compares different…