Computing a Sparse Projection into a Box

04/11/2022
by   Dominique Orban, et al.
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We describe a procedure to compute a projection of w ∈ℝ^n into the intersection of the so-called zero-norm ball k 𝔹_0 of radius k, i.e., the set of k-sparse vectors, with a box centered at a point of k 𝔹_0. The need for such projection arises in the context of certain trust-region methods for nonsmooth regularized optimization. Although the set into which we wish to project is nonconvex, we show that a solution may be found in O(n log(n)) operations. We describe our Julia implementation and illustrate our procedure in the context of two trust-region methods for nonsmooth regularized optimization.

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