projection_nb {sharpPen}

Projection operator for norm balls.

Description

Compute the projection operator for norm balls. For example, we construct

\lambda P_{B_{\| \cdot \|_*}[0,r]}(x/\lambda) = projection_nb(\lambda,r,\| \cdot \|_*,x)

, where \| \cdot \|_* can be l_{1}-norm, l_{2}-norm, and l_{\infty}-norm.

Usage

projection_nb(
lambda,radius,family=c("norm2","norm1","norminf"),
input)

Arguments

lambda

parameter \lambda in the above equation

radius

parameter r in the above equation

family

select the norm ball type, can be l_{1}-norm, l_{2}-norm, and l_{\infty}-norm.

input

input x in the above equation

Details

Take x as input, \lambda and r as parameters. Calculate \lambda P_{B_{\| \cdot \|_*}[0,r]}(x/\lambda) for a given norm ball type.

Value

projection

\lambda P_{B_{\| \cdot \|_*}[0,r]}(x/\lambda)

Author(s)

D.Wang and W.J.Braun

Examples

set.seed(1234567)
family <- "norm1"
temp_p1<-rep(10,100)
projection_nb(3,1,family=family,temp_p1)