Towards An Efficient Approach for the Nonconvex $\ell_p$ Ball Projection: Algorithm and Analysis. (arXiv:2101.01350v6 [math.OC] UPDATED)

Web: http://arxiv.org/abs/2101.01350

This paper primarily focuses on computing the Euclidean projection of a
vector onto the $\ell_{p}$ ball in which $p\in(0,1)$. Such a problem emerges as
the core building block in statistical machine learning and signal processing
tasks because of its ability to promote the sparsity of the desired solution.
However, efficient numerical algorithms for finding the projections are still
not available, particularly in large-scale optimization. To meet this
challenge, we first derive the first-order necessary optimality conditions of
this problem. Based …

algorithm analysis arxiv math projection