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).

# 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)
}