CVXR (version 1.0-14)

mixed_norm: Mixed Norm

Description

\(l_{p,q}(x) = \left(\sum_{i=1}^n (\sum_{j=1}^m |x_{i,j}|)^{q/p}\right)^{1/q}\).

Usage

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

Value

An Expression representing the \(l_{p,q}\) norm of the input.

Arguments

X

An Expression, vector, or matrix.

p

The type of inner norm.

q

The type of outer norm.

Examples

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)