norm1 function

1-Norm

$\|x\|_1 = \sum_{i=1}^n |x_i|$. methods

norm1(x, axis = NA_real_, keepdims = FALSE)

Arguments

• x: An Expression , vector, or matrix.
• axis: (Optional) The dimension across which to apply the function: 1 indicates rows, 2 indicates columns, and NA indicates rows and columns. The default is NA.
• keepdims: (Optional) Should dimensions be maintained when applying the atom along an axis? If FALSE, result will be collapsed into an $n x 1$ column vector. The default is FALSE.

Returns

An Expression representing the 1-norm of the input.

Examples

a <- Variable()
prob <- Problem(Minimize(norm1(a)), list(a <= -2))
result <- solve(prob)
result$value
result$getValue(a)

prob <- Problem(Maximize(-norm1(a)), list(a <= -2))
result <- solve(prob)
result$value
result$getValue(a)

x <- Variable(2)
z <- Variable(2)
prob <- Problem(Minimize(norm1(x - z) + 5), list(x >= c(2,3), z <= c(-1,-4)))
result <- solve(prob)
result$value
result$getValue(x[1] - z[1])