nlminb with more constraints

["John Pitchard" <johnpitchard@googlemail.com>]

 

Dear all,

 

Thanks to those that replied to my last mail about nlminb. I have another question related to nlminb. I'm trying to calculate the optimal asset mix of a portfolio - the asset mix proportions are values between 0 and 1 and the sum of the asset mix proportions sum to 1, e.g. if x(1),..., x(n) are asset mix proportions then each 0<=x(i)<=1 and x(1)+...+x(n)=1.

 

I'm trying to minimise the 95th percentile of a calculated distribution (call this PERCENT(95), thus my objective function is to min PERCENT(95)). However, I want the mean of the distribution to be greater than a specific value, e.g. MEAN>=c, where c is some constant.

 

I would like to know how to achieve this using S-Plus? Should I be minimising the following:

 

objective = PERCENT(95) - lambda(MEAN - c)

 

using a Lagrange multiplier.

 

Any help would be much appreciated.

 

Regards,

John