| Texto completo | |
| Autor(es): |
Armijo, Nicolas F.
;
Bello-Cruz, Yunier
;
Haeser, Gabriel
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Linear Algebra and its Applications; v. 665, p. 24-pg., 2023-02-22. |
| Resumo | |
This paper is devoted to studying the global and finite conver-gence of the semi-smooth Newton method for solving a piece -wise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first provide a negative answer via a counterexample to a con-jecture on the global and finite convergence of the Newton iteration for symmetric and positive definite matrices. Ad-ditionally, we discuss some surprising features of the semi -smooth Newton iteration in low dimensions and its behavior in higher dimensions. Secondly, we present two iterative schemes inspired by the classical Jacobi and Gauss-Seidel methods for linear systems of equations for finding a solution to the prob-lem. We study sufficient conditions for the convergence of both proposed procedures, which are also sufficient for the exis-tence and uniqueness of solutions to the problem. Lastly, we perform some computational experiments designed to illus-trate the behavior (in terms of CPU time) of the proposed iterations versus the semi-smooth Newton method for dense and sparse large-scale problems. Moreover, we included the numerical solution of a discretization of the Boussinesq PDE modeling a two-dimensional flow in a homogeneous phreatic aquifer.(c) 2023 Published by Elsevier Inc. (AU) | |
| Processo FAPESP: | 19/13096-2 - Medidas de complementaridade em condições de otimalidade |
| Beneficiário: | Nicolas Esteban Fuentealba Armijo |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado Direto |
| Processo FAPESP: | 18/24293-0 - Métodos computacionais de otimização |
| Beneficiário: | Sandra Augusta Santos |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |