In the two-parameter case there could be multiple solutions without a trivial relationship between them (so the fix_index trick is not sufficient). It would be good to have a mechanism for selecting one. Unfortunately I'm not sure whether there's a general way of doing this that preserves the nice properties of the problem---simply tacking on an extra objective term might work for some cases but I doubt it's a general solution.
In the two-parameter case there could be multiple solutions without a trivial relationship between them (so the fix_index trick is not sufficient). It would be good to have a mechanism for selecting one. Unfortunately I'm not sure whether there's a general way of doing this that preserves the nice properties of the problem---simply tacking on an extra objective term might work for some cases but I doubt it's a general solution.