y=rnorm(1000, mean = 0, sd = 1.2)
normal.lik1<-function(theta,y){
mu<-theta[1]
sigma2<-theta[2]
n<-length(y)
logl<- -.5*n*log(2*pi) -.5*n*log(sigma2) -(1/(2*sigma2))*sum((y-mu)**2)
return(-logl)
}
optim(c(0,1),normal.lik1,method="BFGS",y=y)
$par
[1] -0.01019272 1.47463370
$value
[1] 1613.034
$counts
function gradient
18 6
$convergence
[1] 0
$message
NULL
#box-constrained optimisation
optim(c(0,1),normal.lik1,method="L-BFGS-B",y=y,lower=c(-Inf,0),upper=c(Inf,Inf))
$par
[1] -0.01020554 1.47430926
$value
[1] 1613.034
$counts
function gradient
10 10
$convergence
[1] 0
$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"
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