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• W1567357472 abstract "This article is concerned with the question of constructing efficient multigrid preconditioners for the linear systems arising when applying semi-smooth Newton methods to large-scale linear-quadratic optimization problems constrained by smoothing operators with box-constraints on the controls. It is shown that, for certain discretizations of the optimization problem, the linear systems to be solved at each semi-smooth Newton iteration reduce to inverting principal minors of the Hessian of the associated unconstrained problem. As in the case when box-constraints on the controls are absent, the multigrid preconditioner introduced here is shown to increase in quality as the mesh-size decreases, resulting in a number of iterations that decreases with mesh-size. However, unlike the unconstrained case, the spectral distance between the preconditioners and the Hessian is shown to be of suboptimal order in general." @default.
• W1567357472 created "2016-06-24" @default.
• W1567357472 creator A5016752483 @default.
• W1567357472 date "2013-11-20" @default.
• W1567357472 modified "2023-09-27" @default.
• W1567357472 title "Multigrid preconditioning of linear systems for semi-smooth Newton methods applied to optimization problems constrained by smoothing operators" @default.
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• W1567357472 doi "https://doi.org/10.1080/10556788.2013.854356" @default.
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