Search results for "Gradient method"
showing 10 items of 38 documents
Electromagnetic Sensitivity Analysis and Shape Optimization Using Method of Moments and Automatic Differentiation
2009
Sensitivity analysis is an important part of gradient-based optimization of electromagnetic devices. We demonstrate how sensitivity analysis can be incorporated into an existing in-house method of moments solver with a relatively small amount of labor by using a technique called automatic differentiation (AD). This approach enables us to obtain (geometrical) sensitivities of the discrete solution with accuracy up to numerical precision. We compare the assembly time and memory usage of the modified and original solvers. Moreover, we optimize the shape of a dipole antenna and the dimensions of a Yagi-Uda array using the presented AD technique, traditional response level finite difference sens…
On a global superconvergence of the gradient of linear triangular elements
1987
Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.
Average Performance Analysis of the Stochastic Gradient Method for Online PCA
2019
International audience; This paper studies the complexity of the stochastic gradient algorithm for PCA when the data are observed in a streaming setting. We also propose an online approach for selecting the learning rate. Simulation experiments confirm the practical relevance of the plain stochastic gradient approach and that drastic improvements can be achieved by learning the learning rate.
Time-harmonic solution for acousto-elastic interaction with controllability and spectral elements
2010
The classical way of solving the time-harmonic linear acousto-elastic wave problem is to discretize the equations with finite elements or finite differences. This approach leads to large-scale indefinite complex-valued linear systems. For these kinds of systems, it is difficult to construct efficient iterative solution methods. That is why we use an alternative approach and solve the time-harmonic problem by controlling the solution of the corresponding time dependent wave equation. In this paper, we use an unsymmetric formulation, where fluid-structure interaction is modeled as a coupling between pressure and displacement. The coupled problem is discretized in space domain with spectral el…
Quasi-Newton approach to nonnegative image restorations
2000
Abstract Image restoration, or deblurring, is the process of attempting to correct for degradation in a recorded image. Typically the blurring system is assumed to be linear and spatially invariant, and fast Fourier transform (FFT) based schemes result in efficient computational image restoration methods. However, real images have properties that cannot always be handled by linear methods. In particular, an image consists of positive light intensities, and thus a nonnegativity constraint should be enforced. This constraint and other ways of incorporating a priori information have been suggested in various applications, and can lead to substantial improvements in the reconstructions. Neverth…
Optimization of the domain in elliptic variational inequalities
1988
This paper is concerned with a nonsmooth shape optimization problem for the Signorini unilateral boundary-value problem. The necessary optimality conditions are derived. The results of computations are presented.
A second-order sparse factorization method for Poisson's equation with mixed boundary conditions
1992
Abstract We propose an algorithm for solving Poisson's equation on general two-dimensional regions with an arbitrary distribution of Dirichlet and Neumann boundary conditions. The algebraic system, generated by the five-point star discretization of the Laplacian, is solved iteratively by repeated direct sparse inversion of an approximating system whose coefficient matrix — the preconditioner — is second-order both in the interior and on the boundary. The present algorithm for mixed boundary value problems generalizes a solver for pure Dirichlet problems (proposed earlier by one of the authors in this journal (1989)) which was found to converge very fast for problems with smooth solutions. T…
Conjugate Gradient Method for Brain Magnetic Resonance Images Segmentation
2018
Part 8: Pattern Recognition and Image Processing; International audience; Image segmentation is the process of partitioning the image into regions of interest in order to provide a meaningful representation of information. Nowadays, segmentation has become a necessity in many practical medical imaging methods as locating tumors and diseases. Hidden Markov Random Field model is one of several techniques used in image segmentation. It provides an elegant way to model the segmentation process. This modeling leads to the minimization of an objective function. Conjugate Gradient algorithm (CG) is one of the best known optimization techniques. This paper proposes the use of the nonlinear Conjugat…
Online Hyperparameter Search Interleaved with Proximal Parameter Updates
2021
There is a clear need for efficient hyperparameter optimization (HO) algorithms for statistical learning, since commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate. Previously existing gradient-based HO algorithms that rely on the smoothness of the cost function cannot be applied in problems such as Lasso regression. In this contribution, we develop a HO method that relies on the structure of proximal gradient methods and does not require a smooth cost function. Such a method is applied to Leave-one-out (LOO)-validated Lasso and Group Lasso, and an online variant is proposed. Numerical experiments corroborate the convergence …
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
1999
We present a new method for solving total variation (TV) minimization problems in image restoration. The main idea is to remove some of the singularity caused by the nondifferentiability of the quantity $|\nabla u|$ in the definition of the TV-norm before we apply a linearization technique such as Newton's method. This is accomplished by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u. Our method can be viewed as a primal-dual method as proposed by Conn and Overton [ A Primal-Dual Interior Point Method for Minimizing a Sum of Euclidean Norms, preprint,…