Density-based Globally Convergent Trust-region Methods for Self-consistent Field Electronic Structure Calculations

Francisco, Juliano B.; Martínez, José Mário; Martı́nez, Leandro

doi:10.1007/s10910-006-9058-0

Cited by 23 publications

(19 citation statements)

References 24 publications

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“…In Figure 1 we exhibit the comparison between the Inexact Restoration method described in this paper, the Levenberg-Marquardt (LM) (also called trust-region) method described in [9] and the classical SCF-DIIS method. In Figure 1a we consider that a method solved the problem when it stopped at a point satisfying (73).…”

Section: Performance Profilesmentioning

confidence: 99%

“…We studied the behavior of the Inexact Restoration algorithms in some typical electronic structure calculations arising in computational chemistry (from now on called "easy" problems) and in some designed problems known to display convergence instabilities [8,9] (called "hard" problems). Easy problems are standard organic molecules Carbon dioxide, Ethylene, Ethanol and Benzene, and some common biologically relevant molecules, as Alanine, Alanine dipeptide, Histidine and Tyrosine.…”

Section: Electronic Structure Calculationsmentioning

confidence: 99%

“…These easy examples were selected to illustrate the behavior of the algorithms in problems for which convergence is usually straightforward. On the other side, we also performed tests on some electronic structure calculations known to display multiple local minima and convergence problems: CrC, Cr 2 , Rh 2 and an arrangement of atoms of formula Li 9 F 9 [8,9].…”

Section: Electronic Structure Calculationsmentioning

confidence: 99%

“…However, the SCF-DIIS algorithm is very successful in many problems and its employment is widely extended in practical calculations. The Optimal Damping Algorithm (ODA) [7] and the trust-region methods given in [8,9] can be proved to be convergent, under different assumptions, to stationary points of (3,4). Other methods that incorporate trust-region concepts were given in [10,11].…”

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Inexact restoration method for minimization problems arising in electronic structure calculations

et al. 2010

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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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Section: Performance Profilesmentioning

confidence: 99%

Section: Electronic Structure Calculationsmentioning

confidence: 99%

Section: Electronic Structure Calculationsmentioning

confidence: 99%

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confidence: 99%

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Inexact restoration method for minimization problems arising in electronic structure calculations

et al. 2010

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“…This method is applicable to convex constrained problems in which the projection on the feasible set is easy to compute. Since its appearance, the method has been intensively used in applications [3,6,10,14,15,19,20,24,26,35,42,50,59,63,64,65,69]. Moreover, it has been the object of several spectral-parameter modifications, alternative nonmonotone strategies have been suggested, convergence and stability properties have been elucidated and it has been combined with other algorithms for different optimization problems.…”

Section: Introductionmentioning

confidence: 99%