Result: Interval algorithms for finding the minimal root in a set of multiextremal one-dimensional nondifferentiable functions

Title:
Interval algorithms for finding the minimal root in a set of multiextremal one-dimensional nondifferentiable functions
Authors:
CASADO, L. G, GARCIA, I, SERGEYEV, Ya. D
Source:
SIAM journal on scientific computing (Print). 24(2):359-376
Publisher Information:
Philadelphia, PA: Society for Industrial and Applied Mathematics, 2003.
Publication Year:
2003
Physical Description:
print, 24 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Généralités, General topics, Analyse de l'erreur, Error analysis, Equations algébriques et transcendantes non linéaires, Nonlinear algebraic and transcendental equations, Méthodes numériques en programmation mathématique, optimisation et calcul variationnel, Numerical methods in mathematical programming, optimization and calculus of variations, Programmation mathématique numérique, Numerical methods in mathematical programming, Analyse algorithme, Algorithm analysis, Análisis algoritmo, Calcul automatique, Computing, Cálculo automático, Domaine recherche, Research field, Dominio investigación, Méthode numérique, Numerical method, Método numérico, Méthode optimisation, Optimization method, Método optimización, Méthode réduction, Reduction method, Método reducción, Méthode séparation et évaluation, Branch and bound method, Método branch and bound, Performance algorithme, Algorithm performance, Resultado algoritmo, Programmation non linéaire, Non linear programming, Programación no lineal, Racine équation, Equation root, Raíz ecuación, Analyse intervalle, Interval analysis, Fonction multiextrémale, Multiextremal function, Fonction non différentiable, Nondifferentiable function, Racine minimale, Minimal root
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Department of Computer Architecture and Electronics, University of Almería, 04120 Almería, United States
ISI-CNR c/o DEIS, University della Calabria, 87036 Rende (CS), Italy
University of Nizhni, Novgorod, Nizhni Novgorod, Russian Federation
ISSN:
1064-8275
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=14630175
Rights:
Copyright 2003 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.14630175
Database:
PASCAL Archive

Further Information

Two problems arising very often in applications are considered. The first problem consists of finding the minimal root of an analytic one-dimensional function over a given interval. It is supposed that the objective function can be multiextremal and nondifferentiable. Three new algorithms based on interval analysis and branch-and-bound global optimization approaches are proposed for solving this problem. The novelty of the new algorithms is in improving the elimination criteria and the order in which interval and point evaluations are realized. The techniques introduced accelerate the search in comparison with interval analysis methods traditionally used for finding roots of equations. The second problem considered in the paper is a generalization of the first one and deals with the search for the minimal root in a set of multiextremal and nondifferentiable functions. The methods proposed for solving the first problem are generalized for solving the second. The main idea is to use the information obtained from any of the functions to reduce the search domain associated with all the functions. Numerical experiments carried out on a wide set of test functions demonstrate a quite satisfactory performance of the new algorithms in both cases.