^,Expression,numeric-method {CVXR} R Documentation

## Elementwise Power

### Description

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)`.

### Usage

```## 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,… and f(x) = |x|^p, this function is convex, positive, with signed monotonicity. For p < 0 and f(x) =

• x^p for x > 0

• +∞x ≤q 0

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

• x^p for x ≥q 0

• -∞x < 0

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

• x^p for x ≥q 0

• +∞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)
```

[Package CVXR version 1.0-10 Index]