On the Convergence of an Active Set Method for L1 Minimization

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dc.contributor.authorWe, Zaiwenen_US
dc.contributor.authorYin, Wotaoen_US
dc.contributor.authorZhang, Hongchaoen_US
dc.contributor.authorGoldfarb, Donalden_US
dc.date.accessioned2018-06-19T17:46:06Zen_US
dc.date.available2018-06-19T17:46:06Zen_US
dc.date.issued2010-07en_US
dc.date.noteJuly 2010en_US
dc.description.abstractWe analyze an abridged version of the active-set algorithm FPC_AS for solving the L1-regularized least squares problem. The active set algorithm alternatively iterates between two stages. In the first "nonmonotone line search (NMLS)" stage, an iterative first-order method based on "shrinkage" is used to estimate the support at the solution. In the second "subspace optimization"stage, a smaller smooth problem is solved to recover the magnitudes of the nonzero components of the solution x. We show that NMLS itself is globally convergent and the convergence rate is at least R-linearly. In particular, NMLS is able to identify of the zero components of a stationary point after a finite number of steps under some mild conditions. The global convergence of FPC_AS is established based on the properties of NMLS.en_US
dc.format.extent19 ppen_US
dc.identifier.citationWe, Zaiwen, Yin, Wotao, Zhang, Hongchao, et al.. "On the Convergence of an Active Set Method for L1 Minimization." (2010) <a href="https://hdl.handle.net/1911/102164">https://hdl.handle.net/1911/102164</a>.en_US
dc.identifier.digitalTR10-22en_US
dc.identifier.urihttps://hdl.handle.net/1911/102164en_US
dc.language.isoengen_US
dc.titleOn the Convergence of an Active Set Method for L1 Minimizationen_US
dc.typeTechnical reporten_US
dc.type.dcmiTexten_US
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