On diagonally-preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming
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| Title: | On diagonally-preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming |
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| Authors: | Escudero, L. F. |
| Source: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) Qüestiió: quaderns d'estadística i investigació operativa; 1982: Vol.: 6 Núm.: 4; p. 333-349 |
| Publisher Information: | Universitat Politècnica de Barcelona. Centre de Càlcul, 1982. |
| Publication Year: | 1982 |
| Subject Terms: | Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming, Programació (Matemàtica), Mathematical programming, 90 Operations research, mathematical programming::90C Mathematical programming [Classificació AMS], Operations research, Investigació operativa, Classificació AMS::90 Operations research, mathematical programming::90C Mathematical programming |
| Description: | 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. |
| Document Type: | Article |
| File Description: | application/pdf; p. 333-349 |
| Language: | English |
| Access URL: | http://hdl.handle.net/2099/4394 https://hdl.handle.net/2099/4394 http://www.raco.cat/index.php/Questiio/article/view/26412 |
| Rights: | CC BY NC ND |
| Accession Number: | edsair.dedup.wf.002..e61c31bb63ce375b0eccd42f0e7e5ba8 |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | 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. |
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