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)
}