soft.thresholding: Proximal operator of the scaled L1 norm.

In jstarling1/starlib: All of my useful functions.

Description

Computes the proximal operator of the L1 norm:

h(x) = λ ||x||_1 ,

where λ is a scaling factor.

Computes the proximal operator of the L1 norm:

h(x) = λ ||x||_1 ,

where λ is a scaling factor.

Usage

soft.thresholding(x, lambda)

soft.thresholding(x, lambda)

Arguments

x	The input vector
t	The step size
opts	List of parameters, which must include: opts$lambda, the scaling factor of the L1 norm.
x	The input vector
t	The step size
opts	List of parameters, which must include: opts$lambda, the scaling factor of the L1 norm.

Value

The proximal of h at x with step size t, given by

prox_h(x,t) = argmin_u [ t h(u) + 1/2 || x - u ||^2 ]

.

The proximal of h at x with step size t, given by

prox_h(x,t) = argmin_u [ t h(u) + 1/2 || x - u ||^2 ]

.

Examples

prox.l1(c(1,3,-2), 1.5, list(lambda=1))
prox.l1(c(1,3,-2), 1.5, list(lambda=1))

jstarling1/starlib documentation built on May 20, 2019, 2:12 a.m.