[R] Minimization/Optimization under functional constraints

[Uwe Ligges]

On 12.10.2011 20:13, forget_f1 wrote:
> 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.


If monotonicity in beta is given , why not minimize 
(f(x+beta*f(x))*f(x))^2 for beta with the box constrained that beta > 0?

Uwe Ligges



> Thanks!!!
>
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