Agreed, construction adhesive would be sufficient in most applications.

That is what thought too. Have you ever heard of someone putting plywood down first or some type of wood so one could staple/nail the carpet down?

Yes you could do that but it's an expensive way to fix gripper rods to a concrete floor
At the end of the carpets life the adhesive would clean off the floor, if that's a concern.
I've used this method a number of times, with no long term damage to subfloor.

@meiklebin the glue cleans off easy? Any preference of glue? Is it like padding- the more expensive the glue, the longer the adhesiveness lasts?

Look for an adhesive with as few VOCs (volatile organic compounds) as possible. It will be better for your health.

Life has been a little nuts, but I attached the carpet. It came out nice! We ripped up the old stuff and installed new molding since the rubber stuff had to go too. Thanks for your tips!

Thanks for the update. What underpad did you go with? What extras did you need to do for moisture mitigation/testing, etc. These extras really help other people make decisions.

I didn't go with the top of the line padding because of cost. We went with a the next grade under it and thus far it has been great! Granted we only needed carpet in the 2 bedrooms, so it does not get a lot of foot traffic. If we would have gotten it throughout condo, then I would say go the extra mile with padding for the longevity of the material. it is plush and I get lots of compliments on the color and its padding. Its off white with speckles in it. It is great at hiding dirt - lol and car hair. I do have 2 little kitties. (One DSH and a Maine Coon)
Luckily, we don't have moisture problems either (being on the 3rd floor).