On diagonally-preconditioning the truncated-Newton method for super-scale linearly constrained nonlinear programming.

Escudero, Laureano F.. "On diagonally-preconditioning the truncated-Newton method for super-scale linearly constrained nonlinear programming.." Qüestiió 6.3 (1982): 261-281. <http://eudml.org/doc/39999>.

@article{Escudero1982,
abstract = {We present an algorithm for super-scale linearly constrained nonlinear programming (LCNP) based on Newton's method. In large scale programming solving Newton's equation at each iteration can be expensive and may not be justified when far from a local solution; we briefly review the current existing methodologies, such that by classifying the problems in small-scale, super-scale and supra-scale problems we suggest the methods that, based on our own computational experience, are more suitable in each case for coping with the problem of solving Newton's equation. For super-scale problems, the Truncated-Newton method (where an inaccurate solution is computed by using the conjugate-gradient method) is recommended; a diagonal BFGS preconditioning of the gradient is used, so that the number of iterations to solve the equation is reduced. The procedure for updating that preconditioning is described for LCNP when the set of active constraints or the partition of basic, superbasic and non-basic (structural) variables have been changed.},
author = {Escudero, Laureano F.},
journal = {Qüestiió},
keywords = {Programación no lineal; Conjuntos convexos; Método de Newton},
language = {eng},
number = {3},
pages = {261-281},
title = {On diagonally-preconditioning the truncated-Newton method for super-scale linearly constrained nonlinear programming.},
url = {http://eudml.org/doc/39999},
volume = {6},
year = {1982},
}

TY - JOUR
AU - Escudero, Laureano F.
TI - On diagonally-preconditioning the truncated-Newton method for super-scale linearly constrained nonlinear programming.
JO - Qüestiió
PY - 1982
VL - 6
IS - 3
SP - 261
EP - 281
AB - We present an algorithm for super-scale linearly constrained nonlinear programming (LCNP) based on Newton's method. In large scale programming solving Newton's equation at each iteration can be expensive and may not be justified when far from a local solution; we briefly review the current existing methodologies, such that by classifying the problems in small-scale, super-scale and supra-scale problems we suggest the methods that, based on our own computational experience, are more suitable in each case for coping with the problem of solving Newton's equation. For super-scale problems, the Truncated-Newton method (where an inaccurate solution is computed by using the conjugate-gradient method) is recommended; a diagonal BFGS preconditioning of the gradient is used, so that the number of iterations to solve the equation is reduced. The procedure for updating that preconditioning is described for LCNP when the set of active constraints or the partition of basic, superbasic and non-basic (structural) variables have been changed.
LA - eng
KW - Programación no lineal; Conjuntos convexos; Método de Newton
UR - http://eudml.org/doc/39999
ER -