Attached Link: http://en.wikipedia.org/wiki/Newton%27s_method_in_optimization

> Quote - If there is more complex math for calculating the catenary when the heights of the endpoints aren't the same, where can that be found?

You can't solve for a analytically except in a small number of special cases (equal height end points or distance between end points is equal to length of chain), but it is possible to obtain the value by using the equal height solution as a first guess for a "Newton's Method" procedure.

Quote - Or does it not exist?

I never came across an analytical treatment (everything effectively deals with the equal height case).
I was sure that there must be one somewhere, but all I came across was (expensive) programs for calculating the hang of anchor cables for ships and the like.