Supply linear constrain to optimizer

Try reparameterize the function. Replace c1 and c2 by functions such they
return values in the range you want. Hints: use ln(c) instead of c for
returning a positive number; to obtain a range like [a, b], you can use a
4-parameter logistic function,... OK, it's not easy in the present case, but
it is a way to get around your problem.
Best regards,

Philippe Grosjean


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Dear R and S users,

I've been working on fitting finite mixture of negative exponential
distributions using maximum likelihood based on the example given in MASS.
So far I had much success in fitting two components. The problem started
when I tried to extend the procedure to fit three components.
More specifically,

likelihood = sum( ln(c1*exp(-x/lambda1)/lambda1 +
c2*exp(-x/lambda2)/lambda2 + (1-c1-c2)*exp(-x/lambda3)/lambda3) )

I've used optimizers such as ms and nlminb (SPLUS 5.0 for UNIX), and
provided parameters constrains (0 <= c1, c2 <= 1) to nlminb via lower and
upper. But these constrains provide no protection for (1-c1-c2) being
between interval [0,1], which resulted in generating NAs in the likelihood
function during iteration.

I've been looking at various documentations, but didn't see anywhere
mentioning setting linear constrain, in this case, c1 + c2 <= 1.

Any suggestion and pointers will be greatly apprepciated.

Kevin Xie
Research Student
Cavendish School of Computer Science
University of Westminster
London, UK

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