Raises each element of the input to the power \(p\).
If `expr`

is a CVXR expression, then `expr^p`

is equivalent to `power(expr,p)`

.

```
# S4 method for Expression,numeric
^(e1, e2)
power(x, p, max_denom = 1024)
```

## Arguments

- e1
An Expression object to exponentiate.

- e2
The power of the exponential. Must be a numeric scalar.

- x
An Expression, vector, or matrix.

- p
A scalar value indicating the exponential power.

- max_denom
The maximum denominator considered in forming a rational approximation of `p`

.

## Details

For \(p = 0\) and \(f(x) = 1\), this function is constant and positive.
For \(p = 1\) and \(f(x) = x\), this function is affine, increasing, and the same sign as \(x\).
For \(p = 2,4,8,\ldots\) and \(f(x) = |x|^p\), this function is convex, positive, with signed monotonicity.
For \(p < 0\) and \(f(x) = \)

\(x^p\) for \(x > 0\)

\(+\infty\)\(x \leq 0\)

, this function is convex, decreasing, and positive.
For \(0 < p < 1\) and \(f(x) =\)

\(x^p\) for \(x \geq 0\)

\(-\infty\)\(x < 0\)

, this function is concave, increasing, and positivea.
For \(p > 1, p \neq 2,4,8,\ldots\) and \(f(x) = \)

\(x^p\) for \(x \geq 0\)

\(+\infty\)\(x < 0\)

, this function is convex, increasing, and positive.

## Examples

```
if (FALSE) {
x <- Variable()
prob <- Problem(Minimize(power(x,1.7) + power(x,-2.3) - power(x,0.45)))
result <- solve(prob)
result$value
result$getValue(x)
}
```