Cutting planes and a biased Newton direction for minimizing quasiconvex functions

A biased Newton direction is introduced for minimizing quasiconver functions with bounded level sets. It is a generalization of the usual Newton’s direction for strictly convex quadratic functions. This new direction can be derived from the intersection of approzimating hyperplanes to the epigraph a...

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Autores principales: Echebest, Nélida Ester, Guardarucci, María Teresa, Scolnik, Hugo Daniel, Vacchino, María Cristina
Formato: Articulo
Lenguaje:Inglés
Publicado: 2000
Materias:
Matemática
Quasiconvex functions
Level sets
Discretization methods
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/150086
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-150086
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Quasiconvex functions
Level sets
Discretization methods
spellingShingle Matemática
Quasiconvex functions
Level sets
Discretization methods
Echebest, Nélida Ester
Guardarucci, María Teresa
Scolnik, Hugo Daniel
Vacchino, María Cristina
Cutting planes and a biased Newton direction for minimizing quasiconvex functions
topic_facet Matemática
Quasiconvex functions
Level sets
Discretization methods
description A biased Newton direction is introduced for minimizing quasiconver functions with bounded level sets. It is a generalization of the usual Newton’s direction for strictly convex quadratic functions. This new direction can be derived from the intersection of approzimating hyperplanes to the epigraph at points on the boundary of the same level set. Based on that direction, an unconstrained minimization algorithm is presented. It is proved to have global and local-quadratic convergence under standard hypotheses. These theoretical results may lead to different methods based on computing search directions using only first order information at points on the level sets. Most of all if the computational cost can be reduced by relaxing some of the conditions according for instance to the results presented in the Appendix. Some tests are presented to show the qualitative behavior of the new direction and with the purpose to stimulate further research on these kind of algorithms.
format Articulo
Articulo
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 Cutting planes and a biased Newton direction for minimizing quasiconvex functions
title_short Cutting planes and a biased Newton direction for minimizing quasiconvex functions
title_full Cutting planes and a biased Newton direction for minimizing quasiconvex functions
title_fullStr Cutting planes and a biased Newton direction for minimizing quasiconvex functions
title_full_unstemmed Cutting planes and a biased Newton direction for minimizing quasiconvex functions
title_sort cutting planes and a biased newton direction for minimizing quasiconvex functions
publishDate 2000
url http://sedici.unlp.edu.ar/handle/10915/150086
work_keys_str_mv AT echebestnelidaester cuttingplanesandabiasednewtondirectionforminimizingquasiconvexfunctions
AT guardaruccimariateresa cuttingplanesandabiasednewtondirectionforminimizingquasiconvexfunctions
AT scolnikhugodaniel cuttingplanesandabiasednewtondirectionforminimizingquasiconvexfunctions
AT vacchinomariacristina cuttingplanesandabiasednewtondirectionforminimizingquasiconvexfunctions
bdutipo_str Repositorios
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