Why does optimx in R not give the correct solution to this simple nonparametric likelihood maximization?

Is optimx() providing incorrect solution or am I missing a simple point? Thank you!

I am trying to maximize a very simple likelihood. This is a non-parametric likelihood in the sense that the distribution of F is not specified parametrically. Rather, for each observed xi, f(xi)=pi and thus log(Likelihood)=Sum(log(f(xi)))=Sum(log(pi)).

The function I am trying to maximize is: sum(log(pi))+lamda(sum(pi-1)) where sum(pi)=1 (i.e. this is a constrained maximization problem which can be solved using Lagrange multiplier).

The answer to this problem is pi=1/n where n is the number of data points. However, optimx does not seem to give this solution. Does anybody have any idea. If n=2, the function I am maximizing is log(p1)+log(p2)+lamda(p1+p2-1).

Here is my code and output from R:

n=2
log.like=function(p)
{
  lamda=p[n+1]
  ll=0
  for(i in 1:n){
    temp = log(p[i])+lamda*p[i]-lamda/(n)
    ll=ll+temp
  }
  return(-ll)
}


mle = optimx(c(0.48,.52,-1.5),
             log.like,
             lower=c(rep(0.1,2),-3),
             upper=c(rep(.9,2),-1),
             method = "L-BFGS-B")

> mle
             par  fvalues   method fns grs itns conv  KKT1 KKT2 xtimes
1 0.9, 0.9, -1.0 1.010721 L-BFGS-B   8   8 NULL    0 FALSE   NA      0

The solution to the equation when n=2 is p1=p2=1/2 and lamda=-2. However, I do not get this when using optimx. Any idea?