norm1 {CVXR} R Documentation

## 1-Norm

### Description

\|x\|_1 = ∑_{i=1}^n |x_i|.

### Usage

```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`.

### Value

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])
```

[Package CVXR version 1.0-10 Index]