Seminorm-Induced Oblique Projections for Sparse Nonlinear Convex Feasibility Problems

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.