Error in nonlinear optimization problem : infinite or missing values in 'x'

Question

I have to consider optimization problem in simulation study. An instance is given below:

library(mvtnorm)
library(alabama)

n = 200
q = 0.5
X <- matrix(0,         


        

Answer 1

As said before, see Maximizing nonlinear constraints problem using r package nloptr:
You have to prevent the solver to run into an area where your objective function is not defined, here this means p_i >= 0 for each index i. And if it does, let the objective function return some finite value. Simplifying your function (for q = 0.5) it looks, for instance, like

f1 <- function(p) sum(sqrt(pmax(0, p)))

Better also to provide an inequality constraint for p_i > 0 as

heq1 <- function(p) c(sum(x1 * p) - x01, sum(x2 * p) - x02, sum(p) - 1)
hin1 <- function(p) p - 1e-06

Now the solver returns a plausible result:

sol <- alabama::auglag(pInit, fn = function(p) -f1(p), 
                       heq = heq1, hin = hin1)

-1 * sol$value
## [1] 11.47805

and the equality conditions are all satisfied:

heq1(sol$par)
## [1] -4.969690e-09  5.906888e-09  1.808652e-08

All this can be done 'programmatically', with a bit of care, naturally.