Constraints in constrOptim.nl in r - r

Question

I am using R package costrOptim.nl.
I need to minimize a function with the following constraints:
Alpha < sqrt(2*omega) and omega > 0
In my code expressed as:
theta[3] < sqrt(2*theta[1]) and theta[1] > 0
I write these conditions as:
Image
But when I call optimizer and run it.
I'm getting the following problem:
1: In sqrt(2 * theta[1]) : NaNs produced
Why? Did I set the proper conditions?

Answer 1

This is my whole code.
data <- read.delim(file = file, header = FALSE)
ind <- seq(from = 1, to = NROW(data), by = 1)
data <- data.frame(ind = ind, Ret = data$V1, Ret2 = data$V1^2)
colnames(data)[1] <- "Ind"
colnames(data)[2] <- "Ret"
colnames(data)[3] <- "Ret2"
T <- length(data$Ret)
m <- arima(x = data$Ret2, order = c(3,0,0), include.mean = TRUE, method = c("ML"))
b_not <- m$coef
omega <- 0.1
alpha <- 0.005
beta <- 0.9
theta <- c(omega,beta,alpha) # "some" value of theta
s0 <- theta[1]/(1-theta[2])
theta[3] < sqrt(2*theta[1]) # check whether the Feller condition is verified
N <- 30000
reps <- 1
rho <- -0.8
n <- 100
heston.II <- function(theta){
set.seed(5)
u <- rnorm(n = N*reps,mean = 0, sd = 1)
u1 <- rnorm(n = N*reps,mean = 0, sd = 1)
u2 <- rho*u + sqrt((1-rho^2))*u1
sigma <- matrix(0, nrow = N*reps, ncol = 1)
ret.int <- matrix(0, nrow = N*reps, ncol = 1)
sigma[1,1] <- s0
for (i in 2:(N*reps)) {
sigma[i,1] <- theta[1] + theta[2]*sigma[i-1,1] + theta[3]*sqrt(sigma[i-1,1])*u1[i]
# if(sigma[i,1] < 0.00000001){ sigma[i,1] = s0}
}
for (i in 1:(N*reps)) {
ret.int[i,1] <- sqrt(sigma[i,1])*u2[i]
}
ret <- matrix(0, nrow = N*reps/n, ncol = 1)
ret[1,1] <- sum(ret.int[1:n],1)
for (i in 2:((N*reps)/n)) {
ret[i,] <- sum(ret.int[(n*i):(n*(i+1))])
ret[((N*reps)/n),] <- sum(ret.int[(n*(i-1)):(n*i)])
}
ret2 <- ret^2
model <- arima(x = ret2, order = c(3,0,0), include.mean = TRUE)
beta_hat <- model$coef
m1 <- beta_hat[1] - b_not[1]
m2 <- beta_hat[2] - b_not[2]
m3 <- beta_hat[3] - b_not[3]
m4 <- beta_hat[4] - b_not[4]
D <- cbind(m1,m2,m3,m4)
DD <- (D)%*%t(D)/1000
DD <- as.numeric(DD)
return(DD)
}
heston.sim <- heston.II(theta)
hin <- function(theta){
h <- rep(NA, 2)
h[1] <- theta[1]
h[2] <- sqrt(2*theta[1]) - theta[3]
return(h)
}
hin(theta = theta)
.opt <- constrOptim.nl(par = theta, fn = heston.II, hin = hin)
.opt