R linear model with constraints

问题:

I want to fit a linear model

y ~ a_1 * x_1 + ... + a_n * x_n

with parameter constraints

a_1,...,a_n >=0 

and

a_1 + ... + a_n <= 1 

in R.

Is there an elegant and fast way to do that and without using solve.QP of the quadprog package. It would be wonderful if a short but detailed use case would be outlined for a proposed solution.

回答1:

You can use constrOptim with cost function least square and contraints defined such that ui %*% a >= ci.

Suppose n=3. You want constraints such as:

 a1         >=  0
     a2     >=  0
         a3 >=  0
-a1 -a2 -a3 >= -1

Thus you have to provide constrOptim the following parameters:

ui = rbind(c(1,0,0),
           c(0,1,0),
           c(0,0,1),
           c(-1,-1,-1))

ci = c(0,0,0,-1)

Set also explicitely grad=NULL in constrOptim if you do not use the gradient.

Hope it helps.