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13.334 Articles in journals published by the UPC
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  • Qüestiió (Quaderns d'estadística i investigació operativa)
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On diagonally-preconditioning the 2-steps BFGS method with accumulated steps for supra-scale linearly constrained nonlinear programming

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Escudero, L. F.
Document typeArticle
Defense date1982-12
PublisherUniversitat Politècnica de Barcelona. Centre de Càlcul
Rights accessOpen Access
Attribution-NonCommercial-NoDerivs 2.5 Spain
Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 2.5 Spain
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.
URIhttp://hdl.handle.net/2099/4394
ISSN0210-8054 (versió paper)
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  • Qüestiió (Quaderns d'estadística i investigació operativa) - 1982, vol. 6, núm. 4 [6]
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