Search results for "Gradient method"
showing 8 items of 38 documents
Parametric Design of Sailing Hull Shapes
2006
The author presents an original algorithm aimed at automatically generating the hull shape of a sailing yacht starting from an initial set of parameters. The procedure consists of two steps. First one keel line and a Designed Water Line (DWL in the following) are faired according to a set of parameters, say length of water line, canoe body draft, stem angle and some adimensional coefficients. This information is then used to fair the hull surface, which must in turn fulfil more prerequisites (parameters like displaty cement, floatation area and related coefficients). The hull is defined by means of a B-spline surface, the fairing of which is ensured by allowing for all the imposed objective…
Multilayer neural networks: an experimental evaluation of on-line training methods
2004
Artificial neural networks (ANN) are inspired by the structure of biological neural networks and their ability to integrate knowledge and learning. In ANN training, the objective is to minimize the error over the training set. The most popular method for training these networks is back propagation, a gradient descent technique. Other non-linear optimization methods such as conjugate directions set or conjugate gradient have also been used for this purpose. Recently, metaheuristics such as simulated annealing, genetic algorithms or tabu search have been also adapted to this context.There are situations in which the necessary training data are being generated in real time and, an extensive tr…
Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring
2013
We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems, such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state-of-the-art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional precondi…
An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes
2013
This study considers developing numerical solution techniques for the computer simulations of time-harmonic fluid-structure interaction between acoustic and elastic waves. The focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements. We concentrate on the model, in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement.Traditionally, the complex-valued time-harmonic equations are used for solving the time-harmonic problems. Instead of that, we focus on finding periodic solutions without solving the time-harmonic problem…
Optimal Heating of an Indoor Swimming Pool
2020
This work presents the derivation of a model for the heating process of the air of a glass dome, where an indoor swimming pool is located in the bottom of the dome. The problem can be reduced from a three dimensional to a two dimensional one. The main goal is the formulation of a proper optimization problem for computing the optimal heating of the air after a given time. For that, the model of the heating process as a partial differential equation is formulated as well as the optimization problem subject to the time-dependent partial differential equation. This yields the optimal heating of the air under the glass dome such that the desired temperature distribution is attained after a given…
CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS
2018
We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…
A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising
2015
Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from ex…
Evaluating the performance of artificial neural networks for the classification of freshwater benthic macroinvertebrates
2014
Abstract Macroinvertebrates form an important functional component of aquatic ecosystems. Their ability to indicate various types of anthropogenic stressors is widely recognized which has made them an integral component of freshwater biomonitoring. The use of macroinvertebrates in biomonitoring is dependent on manual taxa identification which is currently a time-consuming and cost-intensive process conducted by highly trained taxonomical experts. Automated taxa identification of macroinvertebrates is a relatively recent research development. Previous studies have displayed great potential for solutions to this demanding data mining application. In this research we have a collection of 1350 …