Accelerated Gradient Descent Method for Projections onto the ℓ1-Ball - Rodríguez, P. (Institute of Electrical and Electronics Engineers, 2018)
We present a computationally efficient algorithm to solve the projection onto the ℓ 1 -ball problem, which is cast as an equivalent univariate optimization problem by means of its dual formulation, the ℓ ∞ proximity operator. Our algorithm, which is a customization of the Nesterov's accelerated gradient descent method, is empirically demonstrated to be faster than the state-of-the-art methods for the projection onto the ℓ 1 -ball problem.
Keywords: Ball (mathematics); Gradient descent; Stochastic gradient descent; Algorithm; Projection (relational algebra); Computer science; Univariate; Mathematics; Combinatorics; Artificial intelligence; Multivariate statistics; Mathematical analysis; Machine learning; Artificial neural network; https://purl.org/pe-repo/ocde/ford#1.01.02