Optimization in R: constrOptim not converging - r

Question

I am looking at a way to optimize a function in R having several constraints. That's a piece of cake using Excel but I cannot make it work in R.
What I want is to find the set of parameters that maximizes a function under the contraints that parameters should be non-increasing and that the sum of parameters x_i ...x_max is bound for each i.
I wrote a simple example. It works for two parameters but not for three. For three parameters it looks like the optimization procedure is not doing anything.
In real-life cases I would like to use between 12 and 120 parameters so I am a bit worried it does not work with 3 ...
So any help is welcome ... and thanks in advance for the (eventual) reply.
The code for two parameters is (working)
Omp <- function (p)
{
calc <- -p[1]-2*p[2]
return (calc)
}
ui1 <-matrix(c(-1,0,1,-1,-1,-1),ncol =2)
ci1 <-c(-100,-70,0)-0.0000001
init1 <-c(100,0)
(ui1 %*% init1) - ci1
tst <- constrOptim(init1, Omp, grad = NULL, ui = ui1, ci = ci1)
The output is conform expectations:
> sum(tst$par)
[1] 100
> tst$par
[1] 50 50
The code for 3 parameters is (not working)
Opm <- function (p)
{
calc <- -p[1]-2*p[2]-3*p[3]
print(calc)
return (calc)
}
ui1 <-matrix(c(-1,0,0,1,0,-1,-1,0,-1,1,-1,-1,-1,0,-1),ncol =3)
ci1 <-c(-100,-70,0,0,0)-0.0000001
init1 <-c(65,35,0)
(ui1 %*% init1) - ci1
tst <- constrOptim(init1, Opm, grad = NULL, ui = ui1, ci = ci1)
It runs but always remains close to the initial guess.
> tst$par
[1] 6.500000e+01 3.500000e+01 9.685755e-08

Answer 1

Someone else may be able to provide more insight, but your starting values may not be far enough inside the feasible region.
As you stated, this does not produce the expected result:
ui1 <-matrix(c(-1,0,0,1,0,-1,-1,0,-1,1,-1,-1,-1,0,-1),ncol =3)
ci1 <-c(-100,-70,0,0,0)-0.0000001
init1 <-c(65,35,0)
(ui1 %*% init1) - ci1
tst <- constrOptim(init1, Opm, grad = NULL, ui = ui1, ci = ci1)
round(tst$par)
[1] 65 35 0
But adjusting the small offset in ci1 slightly, I get a different result - similar to your expectations in your first example.
ci1 <-c(-100,-70,0,0,0)-0.00001
init1 <-c(65,35,0)
(ui1 %*% init1) - ci1
tst <- constrOptim(init1, Opm, grad = NULL, ui = ui1, ci = ci1)
round(tst$par)
[1] 50 50 0