Have you considered using the optim function with L-BFGS-B for bounded
optimization. Obviously, you will have to do changes of variables so that
everything is in terms of a rectangle (which is the type of bounding that it
accepts).

I believe it is based on "A LIMITED MEMORY ALGORITHM FOR BOUND CONSTRAINED
OPTIMIZATION" By Richard H Byrd,  Peihuang Lu, Jorge Nocedal, and Ciyou Zhu.
Technical Report NAM-08, May 1994.

They also have a paper on the exact implementation. I also believe that R
uses the code from Nocedal et al.
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