Inexact restoration method for minimization problems arising in electronic structure calculations

Autor(es)

Francisco, Juliano B. ^[1] ; Martinez, J. M. ^[2] ; Martinez, Leandro ^[3] ; Pisnitchenko, Feodor ^[2]

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

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