On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.

Título inglés	On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.
Título español	Precondicionamiento diagonal del método BFGS de 2 etapas con etapas acumuladas para programación no lineal restringida linealmente en supraescala.
Autor/es	Escudero, Laureano F.
Organización	Cent. Invest. UAM-IBM, Madrid, España
Revista	0210-8054
Publicación	1982, 6 (4): 333-349, 24 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	We present an algorithm for supra-scale linearly constrained nonlinear programming (LNCP) based on the Limited-Storage Quasi-Newton's method. In large-scale programming solving the reduced Newton equation at each iteration can be expensive and may not be justified when far from a local solution; besides, the amount of storage required by the reduced Hessian matrix, and even the computing time for its Quasi-Newton approximation, may be prohibitive. An alternative based on the reduced Truncated-Newton methodology, that has been proved to be satisfactory for super-scale problems, is not recommended for supra-scale problems since it requires an additional gradient evaluation and the solving of two systems of linear equations per each minor iteration. It is recommended a 2-steps BFGS approximation of the inverse of the reduced Hessian matrix such that it does not require to store any matrix since the product matrix-vector is the vector to be approximated; it uses the reduced gradient and solution related to the two previous iterations and the so-termed restart iteration. A diagonal direct BFGS preconditioning is used.
Clasificación UNESCO	120711
Palabras clave español	Algoritmos ; Programación no lineal ; Método de Newton
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