An $\mathcal{O}(n\log n)$ projection operator for weighted $\ell_1$-norm regularization with sum constraint

This work addresses a computational bottleneck in optimization for researchers and practitioners using weighted ℓ1-norm regularization, but it is incremental as it builds on existing projection methods.

The paper tackled the problem of efficiently computing the projection operator for weighted ℓ1-norm regularization with a sum constraint, and provided an algorithm with O(n log n) time complexity along with an elementary proof.