r - How can I find a maximum to this equation -

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i have function find it's maximum

deposit_likelood <- function(a1,a2) { (0.5672 - 0.092 * a1 + 0.0044 * a2^2 }

how can maximize deposit_likelood while a1 should between -3 , +3 , a2 should between 0.5 , 0.9 ?

i tried use optimize() function:

optimize(deposit_likelood, interval=c(-3,3,0.5,0.9), maximum=true)

but got error :

error in a2^2 : 'a2' missing

i hoping work out hints (because thats better way learn) here go.

note i've had change function because question didn't have valid function in it, , unpack arguments:

> deposit_likelood = function(a) {a1=a[1];a2=a[2];return (0.5672 - 0.092 * a1 + 0.0044 * a2^2) }

we give optim start point (somewhere in box constraints), tell use method box constraints, , specify constraints:

> optim(c(0,.7),deposit_likelood,method="l-bfgs-b",lower=c(-3,.5), upper=c(3,.9), control=list(fnscale=-1)) $par [1] -3.0  0.9  $value [1] 0.846764  $counts function gradient         7        7   $convergence [1] 0  $message [1] "convergence: norm of projected gradient <= pgtol"

the return value has $par values of a1 , a2 respectively. $convergence code 0 tells worked okay.


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