On diagonally-preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming
Visualitza/Obre
Tipus de documentArticle
Data publicació1982-12
EditorUniversitat Politècnica de Barcelona. Centre de Càlcul
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
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.
ISSN0210-8054 (versió paper)
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
article.pdf | 950,0Kb | Visualitza/Obre |