proximal operator – Optimization Online

Minimization of L1 over L2 for sparse signal recovery with convergence guarantee

Published: 2020/10/17, Updated: 2021/06/15

Applications - OR and Management Sciences alternating direction method of multipliers, global convergence, linear convergence, nonconvex optimization, proximal operator, sparsity

The ratio of the $L_1$ and $L_2$ norms, denoted by $L_1/L_2$, becomes attractive due to its scale-invariant property when approximating the $L_0$ norm to promote sparsity. In this paper, we incorporate the $L_1/L_2$ formalism into an unconstrained model in order to deal with both noiseless and noisy observations. To design an efficient algorithm, we derive … Read more

An (n\log(n))$ Algorithm for Projecting Onto the Ordered Weighted $\ell_1$ Norm Ball

Published: 2015/03/31, Updated: 2015/06/26

Damek Davis

Convex and Nonsmooth Optimization octogonal shrinkage and clustering algorithm for regression, ordered weighted $\ell_1$ norm, projection operator, proximal operator

The ordered weighted $\ell_1$ (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm. This norm has desirable statistical properties and can be used to perform simultaneous clustering and regression. In this paper, we show how to compute the projection of an $n$-dimensional vector onto the OWL … Read more