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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

Inexact restoration method for minimization problems arising in electronic structure calculations

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Autor(es):
Francisco, Juliano B. [1] ; Martinez, J. M. [2] ; Martinez, Leandro [3] ; Pisnitchenko, Feodor [2]
Número total de Autores: 4
Afiliação do(s) autor(es):
[1] Univ Fed Santa Catarina, Dept Math, BR-88040900 Florianopolis, SC - Brazil
[2] Univ Estadual Campinas, Dept Appl Math, Campinas, SP - Brazil
[3] Univ Estadual Campinas, Inst Chem, Campinas, SP - Brazil
Número total de Afiliações: 3
Tipo de documento: Artigo Científico
Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 50, n. 3, p. 555-590, DEC 2011.
Citações Web of Science: 9
Resumo

An inexact restoration (IR) approach is presented to solve a matricial optimization problem arising in electronic structure calculations. The solution of the problem is the closed-shell density matrix and the constraints are represented by a Grassmann manifold. One of the mathematical and computational challenges in this area is to develop methods for solving the problem not using eigenvalue calculations and having the possibility of preserving sparsity of iterates and gradients. The inexact restoration approach enjoys local quadratic convergence and global convergence to stationary points and does not use spectral matrix decompositions, so that, in principle, large-scale implementations may preserve sparsity. Numerical experiments show that IR algorithms are competitive with current algorithms for solving closed-shell Hartree-Fock equations and similar mathematical problems, thus being a promising alternative for problems where eigenvalue calculations are a limiting factor. (AU)

Processo FAPESP: 05/57684-2 - Lagrangeano aumentado e problemas de equilíbrio
Beneficiário:María Laura Schuverdt
Linha de fomento: Bolsas no Brasil - Pós-Doutorado
Processo FAPESP: 06/53768-0 - Métodos computacionais de otimização
Beneficiário:José Mário Martinez Perez
Linha de fomento: Auxílio à Pesquisa - Temático