R help - Oct 2011 - 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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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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> View this message in context:
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> Sent from the R help mailing list archive at Nabble.com.
>
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> and provide commented, minimal, self-contained, reproducible code.

You can use the DEoptim function in DEoptim package and to include a line of
code within your objective function that assigns a very high value when the
constraints are not satisfied. I have tried that and it works. 

-----
Juan David Ospina Arango

School of Statistics
Universidad Nacional de Colombia, Colombia

Laboratoire de Traitement du Signal et de l'Image
Universit? de Rennes 1, France
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