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

Escudero, Laureano F.. "On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.." Qüestiió 6.4 (1982): 333-349. <http://eudml.org/doc/40000>.

@article{Escudero1982,
abstract = {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.},
author = {Escudero, Laureano F.},
journal = {Qüestiió},
keywords = {Algoritmos; Programación no lineal; Método de Newton},
language = {eng},
number = {4},
pages = {333-349},
title = {On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.},
url = {http://eudml.org/doc/40000},
volume = {6},
year = {1982},
}

TY - JOUR
AU - Escudero, Laureano F.
TI - On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.
JO - Qüestiió
PY - 1982
VL - 6
IS - 4
SP - 333
EP - 349
AB - 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.
LA - eng
KW - Algoritmos; Programación no lineal; Método de Newton
UR - http://eudml.org/doc/40000
ER -