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.
@article{urn:eudml:doc:40000,
title = {On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.},
journal = {Q\"uestii\'o},
volume = {6},
year = {1982},
pages = {333-349},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40000}
}
Escudero, Laureano F. On diagonally preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming.. Qüestiió, Tome 6 (1982) pp. 333-349. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40000/