Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53

This paper develops an idea of H. D. Scolnik for minimizing quasiconvex functions concerning the use of "large steps" based upon geometrical properties of the objective function derived from its level sets. Basically speaking, the increment will be computed by means of auxiliary points suc...

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Detalles Bibliográficos
Autores principales: Echebest, Nélida Ester, Guardarucci, María Teresa, Scolnik, Hugo Daniel, Vacchino, María Cristina
Formato: Publicacion seriada
Lenguaje:Inglés
Publicado: 1993
Materias:
Matemática
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/170315
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-170315
record_format dspace
spelling I19-R120-10915-1703152024-09-18T04:11:08Z http://sedici.unlp.edu.ar/handle/10915/170315 Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53 Echebest, Nélida Ester Guardarucci, María Teresa Scolnik, Hugo Daniel Vacchino, María Cristina 1993 2024-09-17T17:56:01Z en Matemática This paper develops an idea of H. D. Scolnik for minimizing quasiconvex functions concerning the use of "large steps" based upon geometrical properties of the objective function derived from its level sets. Basically speaking, the increment will be computed by means of auxiliary points such that f(xk + hp p) = f(xk) where f(x) is a quasiconvex function and p is an element of a set of directions chosen according to an algorithm which guarantees global and local quadratic convergence. The search direction in each iteration is obtained as the solution of a finite differences system of equations involving the auxiliary directions p and the increments hp , and is Newton's when the function is quadratic. Computational tests are given showing the efficiency of the new algorithm. Material digitalizado en SEDICI gracias a la colaboración de la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP). Facultad de Ciencias Exactas Publicacion seriada Publicacion seriada http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
spellingShingle Matemática
Echebest, Nélida Ester
Guardarucci, María Teresa
Scolnik, Hugo Daniel
Vacchino, María Cristina
Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53
topic_facet Matemática
description This paper develops an idea of H. D. Scolnik for minimizing quasiconvex functions concerning the use of "large steps" based upon geometrical properties of the objective function derived from its level sets. Basically speaking, the increment will be computed by means of auxiliary points such that f(xk + hp p) = f(xk) where f(x) is a quasiconvex function and p is an element of a set of directions chosen according to an algorithm which guarantees global and local quadratic convergence. The search direction in each iteration is obtained as the solution of a finite differences system of equations involving the auxiliary directions p and the increments hp , and is Newton's when the function is quadratic. Computational tests are given showing the efficiency of the new algorithm.
format Publicacion seriada
Publicacion seriada
author Echebest, Nélida Ester
Guardarucci, María Teresa
Scolnik, Hugo Daniel
Vacchino, María Cristina
author_facet Echebest, Nélida Ester
Guardarucci, María Teresa
Scolnik, Hugo Daniel
Vacchino, María Cristina
author_sort Echebest, Nélida Ester
title Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53
title_short Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53
title_full Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53
title_fullStr Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53
title_full_unstemmed Large Steps Discrete Newton Methods for Minimizing Quasiconvex Functions : Notas de Matemática, 53
title_sort large steps discrete newton methods for minimizing quasiconvex functions : notas de matemática, 53
publishDate 1993
url http://sedici.unlp.edu.ar/handle/10915/170315
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AT scolnikhugodaniel largestepsdiscretenewtonmethodsforminimizingquasiconvexfunctionsnotasdematematica53
AT vacchinomariacristina largestepsdiscretenewtonmethodsforminimizingquasiconvexfunctionsnotasdematematica53
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