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

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dc.contributor.authorSantos, S.A.en_US
dc.contributor.authorSorensen, D.C.en_US
dc.date.accessioned2018-06-18T17:42:18Zen_US
dc.date.available2018-06-18T17:42:18Zen_US
dc.date.issued1995-07en_US
dc.date.noteJuly 1995en_US
dc.description.abstractThe trust region subproblem arises frequently in linear algebra and optimization applications. Recently, matrix-free methods have been introduced to solve large-scale trust-region subproblems. These methods only require a matrix-vector product and do not rely on matrix factorizations. These approaches recast the trust-region subproblem in terms of a parameterized eigenvalue problem and then adjust the parameter to find the optimal solution from the eigenvector corresponding to the smallest eigenvalue of the parameterized eigenvalue problem. This paper presents a new matrix-free algorithm for the large-scale trust-region subproblem. The new algorithm improves upon the previous algorithms by introducing a unified iteration that naturally includes the so called hard case. The new iteration is shown to be superlinearly convergent in all cases. Computational results are presented to illustrate convergence properties and robustness of the method.en_US
dc.format.extent39 ppen_US
dc.identifier.citationSantos, S.A. and Sorensen, D.C.. "A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem." (1995) <a href="https://hdl.handle.net/1911/101862">https://hdl.handle.net/1911/101862</a>.en_US
dc.identifier.digitalTR95-20en_US
dc.identifier.urihttps://hdl.handle.net/1911/101862en_US
dc.language.isoengen_US
dc.relation.HasVersionsuperseded by TR99-19en_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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