Power function (with 0<p<1) does not respect DCP rules

[Denizalp Goktas]

I think the power function with exponent 1 > p > 0 does not correctly update the DCP status of an expression. When I look at the CRAN documentation (page 347) I see:

"[the power] function is convex, decreasing, and positive. For 0 < p < 1 and f(x) = x^p for x ≥ 0"

This statement is wrong (unless If I am really missing something) and is not in agreement with the python documentation which states that the power function is "concave, positive, increasing for 0< p < 1 "

Been getting DCP errors on a program and using the is_DCP argument did not help.

[Balasubramanian Narasimhan]

Thanks for the documentation note which we will fix: it is correct, but the typesetting is leading you to read it incorrectly. But what do you base your first statement upon? See below.

> library(CVXR)

Attaching package: ‘CVXR’

The following object is masked from ‘package:stats’:

    power

> x  <- Variable(3)
> p  <- power(x, 0.5)
> is_dcp(p)
[1] TRUE
> is_convex(p)
[1] FALSE
> is_concave(p) 
[1] TRUE