Minimization/Optimization under functional constraints

Hi,

I hope someone can help me with the following issue.

I need find the minimum beta that satisfies the following:

inf{beta>0 | f(x+beta*f(x))*f(x)<=0}

where f() is a function and x is a sample statistic.

Functions such as "nlminb" and "constrOptim" minimize a function and output
the parameter (under parameter constraints).  I need to minimize the
parameter (also constraint) under the functional constraint.  

Obviously,  I can start with a vector for beta (starting from 0) and find
when the switch from >0 to <=0 occurs for the functional argument, but was
wondering if there is a more efficient method/function. 

Thanks!!!

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