A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem

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dc.contributor.authorRojas, Marielbaen_US
dc.contributor.authorSantos, Sandra A.en_US
dc.contributor.authorSorensen, Danny C.en_US
dc.date.accessioned2018-06-18T17:47:33Zen_US
dc.date.available2018-06-18T17:47:33Zen_US
dc.date.issued1999-09en_US
dc.date.noteSeptember 1999en_US
dc.description.abstractWe present a matrix-free algorithm for the large-scale trust-region subproblem. Our algorithm relies on matrix-vector products only and does not require matrix factorizations. We recast the trust-region subproblem as a parameterized eigenvalue problem and compute an optimal value for the parameter. We then find the optimal solution of the trust-region subproblem from the eigenvectors associated with two of the smallest eigenvalues of the parameterized eigenvalue problem corresponding to the optimal parameter. The new algorithm uses a different interpolating scheme than existent methods and introduces a unified iteration that naturally includes the so-called hard case. We show that the new iteration is well defined and convergent at a superlinear rate. We present computational results to illustrate convergence properties and robustness of the method.en_US
dc.format.extent46 ppen_US
dc.identifier.citationRojas, Marielba, Santos, Sandra A. and Sorensen, Danny C.. "A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem." (1999) <a href="https://hdl.handle.net/1911/101924">https://hdl.handle.net/1911/101924</a>.en_US
dc.identifier.digitalTR99-19en_US
dc.identifier.urihttps://hdl.handle.net/1911/101924en_US
dc.language.isoengen_US
dc.titleA New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblemen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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