Displaying similar documents to “First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules”

Converging self-consistent field equations in quantum chemistry – recent achievements and remaining challenges

Konstantin N. Kudin, Gustavo E. Scuseria (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper reviews popular acceleration techniques to converge the non-linear self-consistent field equations appearing in quantum chemistry calculations with localized basis sets. The different methodologies, as well as their advantages and limitations are discussed within the same framework. Several illustrative examples of calculations are presented. This paper attempts to describe recent achievements and remaining challenges in this field.

Abstract variational problems with volume constraints

Marc Oliver Rieger (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Existence results for a class of one-dimensional abstract variational problems with volume constraints are established. The main assumptions on their energy are additivity, translation invariance and solvability of a transition problem. These general results yield existence results for nonconvex problems. A counterexample shows that a naive extension to higher dimensional situations in general fails.

Lagrange multipliers estimates for constrained minimization.

Laureano F. Escudero (1981)

Qüestiió

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We discuss in this work the first-order, second-order and pseudo-second-order estimations of Lagrange multipliers in nonlinear constrained minimization. The paper also justifies estimations and strategies that are used by two nonlinear programming algorithms that are also briefly described.