\(l_{p,q}(x) = \left(\sum_{i=1}^n (\sum_{j=1}^m |x_{i,j}|)^{q/p}\right)^{1/q}\).
mixed_norm(X, p = 2, q = 1)An Expression, vector, or matrix.
The type of inner norm.
The type of outer norm.
An Expression representing the \(l_{p,q}\) norm of the input.
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$value
#> [1] 10
result$getValue(A)
#> [,1] [,2]
#> [1,] 3 4
#> [2,] 3 4
val <- cbind(c(1,4), c(5,6))
prob <- Problem(Minimize(mixed_norm(A,1,Inf)), list(A == val))
result <- solve(prob)
result$value
#> [1] 10.00011
result$getValue(A)
#> [,1] [,2]
#> [1,] 1 5
#> [2,] 4 6