Search results for " Convergence"

Highlighting numerical insights of an efficient SPH method

2018

Abstract In this paper we focus on two sources of enhancement in accuracy and computational demanding in approximating a function and its derivatives by means of the Smoothed Particle Hydrodynamics method. The approximating power of the standard method is perceived to be poor and improvements can be gained making use of the Taylor series expansion of the kernel approximation of the function and its derivatives. The modified formulation is appealing providing more accurate results of the function and its derivatives simultaneously without changing the kernel function adopted in the computation. The request for greater accuracy needs kernel function derivatives with order up to the desidered …

Localization Based on Parallel Robots Kinematics as an Alternative to Trilateration

2022

In this article, a new scheme for range-based localization is proposed. The main goal is to estimate the position of a mobile point based on distance measurements from fixed devices, called anchors, and on inertial measurements. Due to the nonlinear nature of the problem, an analytic relation to compute the position starting from these measurements does not exist, and often trilateration methods are used, generally based on least-square algorithms. The proposed scheme is based on the modeling of the localization process as a parallel robot, thereby methodologies and control algorithms used in the robotic area can be exploited. In particular, a closed-loop control system is designed for trac…

Improving estimation of distribution genetic programming with novelty initialization

2021

Estimation of distribution genetic programming (EDA-GP) replaces the standard variation operations of genetic programming (GP) by learning and sampling from a probabilistic model. Unfortunately, many EDA-GP approaches suffer from a rapidly decreasing population diversity which often leads to premature convergence. However, novelty search, an approach that searches for novel solutions to cover sparse areas of the search space, can be used for generating diverse initial populations. In this work, we propose novelty initialization and test this new method on a generalization of the royal tree problem and compare its performance to ramped half-and-half (RHH) using a recent EDA-GP approach. We f…

The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets

2014

The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …

Disturbed Exploitation compact Differential Evolution for Limited Memory Optimization Problems

2011

This paper proposes a novel and unconventional Memetic Computing approach for solving continuous optimization problems characterized by memory limitations. The proposed algorithm, unlike employing an explorative evolutionary framework and a set of local search algorithms, employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators. The proposed Memetic Computing approach is based on a populationless (compact) evolutionary framework which, instead of processing a population of solutions, handles …

On the Extension of the DIRECT Algorithm to Multiple Objectives

2020

AbstractDeterministic global optimization algorithms like Piyavskii–Shubert, direct, ego and many more, have a recognized standing, for problems with many local optima. Although many single objective optimization algorithms have been extended to multiple objectives, completely deterministic algorithms for nonlinear problems with guarantees of convergence to global Pareto optimality are still missing. For instance, deterministic algorithms usually make use of some form of scalarization, which may lead to incomplete representations of the Pareto optimal set. Thus, all global Pareto optima may not be obtained, especially in nonconvex cases. On the other hand, algorithms attempting to produce r…

A linearization technique and error estimates for distributed parameter identification in quasilinear problems

1996

The identification problem of a nonlinear functional coefficient in elliptic and parabolic quasilinear equations is considered. A distributed observation of the solution of the corresponding equation is assumed to be known a priori. An identification method is introduced, which needs only a linear equation to be solved in each iteration step of the optimization. Estimates of the rate of convergence for the proposed approach are proved, when the equation is discretized with the finite element method with respect to space variables. Some numerical results are given.

2017

Abstract. We present a sensitivity study on transatlantic dust transport, a process which has many implications for the atmosphere, the ocean and the climate. We investigate the impact of key processes that control the dust outflow, i.e., the emission flux, convection schemes and the chemical aging of mineral dust, by using the EMAC model following Abdelkader et al. (2015). To characterize the dust outflow over the Atlantic Ocean, we distinguish two geographic zones: (i) dust interactions within the Intertropical Convergence Zone (ITCZ), or the dust–ITCZ interaction zone (DIZ), and (ii) the adjacent dust transport over the Atlantic Ocean (DTA) zone. In the latter zone, the dust loading show…

When a convergence of filters is measure-theoretic

2022

Abstract Convergence almost everywhere cannot be induced by a topology, and if measure is finite, it coincides with almost uniform convergence and is finer than convergence in measure, which is induced by a metrizable topology. Measures are assumed to be finite. It is proved that convergence in measure is the Urysohn modification of convergence almost everywhere, which is pseudotopological. Extensions of these convergences from sequences to arbitrary filters are discussed, and a concept of measure-theoretic convergence is introduced. A natural extension of convergence almost everywhere is neither measure-theoretic, nor finer than a natural extension of convergence in measure. A straightforw…