Simultaneous subgradient projection algorithms for the convex feasibility problem use subgradient calculations and converge sometimes even in the inconsistent case. We devise an algorithm that uses seminorm-induced oblique projections onto super half-spaces of the convex sets, which is advantageous when the subgradient-Jacobian is a sparse matrix at many iteration points of the algorithm. Using generalized seminorm-induced oblique projections on hyperplanes defined by subgradients at each iterative step, allows component-wise diagonal weighting which has been shown to be useful for early acceleration in the sparse linear case. Convergence for the consistent case with underrelaxation is established.
Citation
in: Y. Censor, M. Jiang and G. Wang (Editors), "Biomedical Mathematics: Promising Directions in Imaging, Therapy Planning and Inverse Problems", Medical Physics Publishing, Madison, WI, USA, 2009, accepted for publication.
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View Seminorm-induced oblique projections for sparse nonlinear convex feasibility problems