`geo_mean` hangs for some values of `p`

[karldw]

Describe the bug For some values of p, the geo_mean() function hangs, seemingly forever. In the example below, it has been using ~100% CPU for several minutes. When I press Ctrl-C to cancel, there is no stack trace.

To Reproduce

library(CVXR)
x = Variable(3)

p_bad = c(0.9, 0.8, 0.7)
m = geo_mean(x, p_bad)   # hangs forever

p_good = c(0.7, 0.8, 0.9)
m = geo_mean(x, p_good)  # runs

Expected behavior I expected geo_mean to run identically in both cases.

Version

CVXR 1.0-1

Session info

``` R version 4.0.2 (2020-06-22) Platform: x86_64-pc-linux-gnu (64-bit) Running under: Ubuntu 20.04.1 LTS Matrix products: default BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/liblapack.so.3 locale: [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8 [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8 [7] LC_PAPER=en_US.UTF-8 LC_NAME=C [9] LC_ADDRESS=C LC_TELEPHONE=C [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: [1] CVXR_1.0-1 loaded via a namespace (and not attached): [1] bit_4.0.4 compiler_4.0.2 R6_2.4.1 Matrix_1.2-18 [5] gmp_0.6-0 Rcpp_1.0.5 bit64_4.0.5 grid_4.0.2 [9] Rmpfr_0.8-1 lattice_0.20-41 ```

[bnaras]

Yes, I see this. I know the current geo_mean implementation is more involved than it needs to be as the comments in the source code (R/atoms.R) indicate. We need a cleaner implementation but a fix should be possible for now.