CVXR (version 0.99-7)

mixed_norm: Mixed Norm

Description

$l_{p,q}(x)={(\sum _{i=1}^n(\sum _{j=1}^m|x_{i,j}|{)}^{q/p})}^{1/q}$.

Usage

mixed_norm(X, p = 2, q = 1)

Arguments

X

An '>Expression, vector, or matrix.

p

The type of inner norm.

q

The type of outer norm.

Value

An '>Expression representing the $l_{p,q}$ norm of the input.

Examples

# NOT RUN {
A <- Variable(2,2)
val <- cbind(c(3,3), c(4,4))
prob <- Problem(Minimize(mixed_norm(A,2,1)), list(A == val))
result <- solve(prob)
result$value
result$getValue(A)

val <- cbind(c(1,4), c(5,6))
prob <- Problem(Minimize(mixed_norm(A,1,Inf)), list(A == val))
result <- solve(prob)
result$value
result$getValue(A)
# }