Dear all,
I have two functions (f1, f2) and 4 unknown parameters (p1, p2, p3, p4). Both
f1 and f2 are functions of p1, p2, and p3, denoted by f1(p1, p2, p3) and
f2(p1,p2,p3) respectively.
The goal is to maximize f1(p1, p2, p3) subject to two constraints:
(1) c = k1*p4/(k1*p4+(1-k1)*f1(p1,p2,p3)), where c and k1 are some known
constants
(2) p4 = f2(p1, p2, p3)
In addition, each parameter ranges from 0 to 1, and both f1 and f2 involve
integrations.
I tried to use lagrange multipliers to eliminate two equality constraints
and then use optim() to find the maximum value and optimal parameter
estimates.
So I let fn be f1+lambda1*(c- k1*p4/(k1*p4+(1-k1)*f1(p1,p2,p3))) +
lambda2(p4-f2(p1,p2,p3)). The error message I got was "Error in fn(par, ...)
: recursive default argument reference."
I wonder whether current build-in functions in R can do this type of jobs.
Any suggestion will be greatly appreciated.
Iris
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