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 = c("stack", "pava"))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
Method used in the prox.
"stack"is a stack-based algorithm (Algorithm 4 in Bogdan et al.)."pava"is the PAVA algorithm used in isotonic regression (also Algorithm 3 in Bogdan et al.).