We describe a procedure to compute a projection of
\(w \in ℝ^n\) 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
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.
Published April 2022 , 15 pages
G2212.pdf (600 KB)