Thanks for your help...actually there is monotonicity in beta so minimizing
the square of the functional constraint works. I verified it with a brute
force search (while loop).
For the sake of knowledge this is what someone else suggested (but didn't
work in my case)
Since x is fixed (given the data), you are really just trying to find
inf{beta>0 | g(beta) <= 0}
where g() is defined in the obvious way.
If you can be sure that the infimum is not 0, then you can get rid of
the constraint beta>0 to transforming the problem to
inf{gamma | h(gamma) <= 0}
where, e.g., h(gamma) = g(exp(gamma)).
Now, if your original f is continuous and isn't constant over any
interval, say, then you could try to solve for the zeros of h, and the
smallest one should be what you're looking for. Finding all the zeros
of h could still be hard of course, and I suspect your problem isn't
that nice anyway or you wouldn't be asking me.
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