power function

Elementwise Power

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). methods

## S4 method for signature '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

## Not run:

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)
## End(Not run)