Abstract
Sparsity optimization for linear least squares problems formulated as non-smooth regularization problems are considered in infinite-dimensional sequence spaces ℓp with p ∈ [0, 1]. Necessary optimality conditions in the format of a complementarity system are obtained. A monotonically convergent scheme is developed for the case p ∈ (0, 1]. For the case p = 0 a primal dual active set strategy based on the Lagrange multiplier rule is proposed and analyzed for special cases.
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