Sorted L1 Proximal Operator

The proximal operator for the Sorted L1 Norm, which is the penalty function in SLOPE. It solves the problem $$ \arg\,\min_x \Big(J(x, \lambda) + \frac{1}{2} ||x - v||_2^2\Big) $$ where \(J(x, \lambda)\) is the Sorted L1 Norm.

Usage

sortedL1Prox(x, lambda, method)

Source

M. Bogdan, E. van den Berg, Chiara Sabatti, Weijie Su, and Emmanuel J. Candès, “SLOPE – adaptive variable selection via convex optimization,” Ann Appl Stat, vol. 9, no. 3, pp. 1103–1140, 2015.

Arguments

x

A vector. In SLOPE, this is the vector of coefficients.

lambda

A non-negative and decreasing sequence of weights for the Sorted L1 Norm. Needs to be the same length as x.

method

DEPRECATED

Value

An evaluation of the proximal operator at x and lambda.