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Inexact restoration method for minimization problems arising in electronic structure calculations

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Abstract

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Federal University of Santa Catarina, Santa Catarina, Brazil

    Juliano B. Francisco

  2. Department of Applied Mathematics, University of Campinas, Campinas, Brazil

    J. M. Martínez

  3. Institute of Chemistry, University of Campinas, Campinas, Brazil

    Leandro Martínez

  4. Department of Applied Mathematics, University of Campinas, Campinas, Brazil

    Feodor Pisnitchenko

Authors
  1. Juliano B. Francisco
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  2. J. M. Martínez
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  3. Leandro Martínez
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  4. Feodor Pisnitchenko
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Corresponding author

Correspondence to J. M. Martínez.

Additional information

This work was supported by PRONEX-Optimization (PRONEX-CNPq/FAPERJ E-26/171.510/2006-APQ1), FAPESP (Grants 2006/53768-0 and 2005/57684-2) and CNPq.

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Francisco, J.B., Martínez, J.M., Martínez, L. et al. Inexact restoration method for minimization problems arising in electronic structure calculations. Comput Optim Appl 50, 555–590 (2011). https://doi.org/10.1007/s10589-010-9318-6

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