[R] MLE Constraints

[LFRC]

Dears,

I'm trying to find the parameters (a,b, ... l) that optimize the function
(Model) 
described below.

1) How can I set some constraints with MLE2 function? I want to set p1>0,
p2>0, 
p3>0, p1>p3. 

2) The code is giving the following warning. 
Warning: optimization did not converge (code 1)
How can I solve this problem?

Can someone help me?

M <- 14
Y = c(0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1)
x1 = c(0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.50, 0.25, 
0.25, 0.25, 0.25)
x2 = c(-1, -1, -1, -1, -1,  1,  1,  1,  1,  1,  1,  1,  1,  1)
x3 = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
states = c(1, 1, 2, 3, 1, 2, 3, 1, 1, 2, 2, 3, 1, 1)
prob_fn = rep(0,M)

Model=function(a, b, c, d, e, f, g, h, i, j, k, l)
{
p1 = exp(-(a   g*x1   d*x2   j*x3))
p2 = exp(-(b   h*x1   e*x2   k*x3))
p3 = exp(-(c   i*x1   f*x2   l*x3))

### Set P
t5 = 0
while(t5<M)
{
t5 = t5 1

if(states[t5]==1)  {prob_ok = p1[1]}
if(states[t5]==2)  {prob_ok = p2[1]}
if(states[t5]==3)  {prob_ok = p3[1]}
prob_fn[t5] = c(prob_ok)
}

prob_fn[prob_fn==0] = 0.0000000000001

### LL
ll_calc = -(sum(Y*log(prob_fn)))
return(ll_calc)
}

res = mle2(Model, start=list(a=1, b=1, c=1, d=0.15, e=0.15,
f=0.15, g=0.9, h=0.9, i=0.9, j=0.1, k=0.1, l=0.1), method = "Nelder-
Mead")
res

Best regards,
LFRC

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