Joseph Meehan writes:

Does anyone what to suggest what kind of product would work with the
type of plastic used in eyeglasses?

http://zennioptical.com/
http://www.optical4less.com/

I love these guys. They make your glasses in Hong Kong and mail them to
you. Good quality at prices not worth the trouble of repairing. No
connection to them myself; I'm just a satisfied customer.

If I were fixing your lenses, I would glue with CA or polyurethane on a
toothpick, and miniature drill and stitch at the ends of the break with 34
gauge stainless wire. The stitches would be ugly, but so's the glue line.

The stainless wire is my latest favorite fix-it trick. All of 6
thousandths thick (literally, 2 red bleep hairs), with 2 pounds of breaking
strength. You can reinforce a lot of geometry that no glue could possibly
hold.