r - fast way to evaluate the maximum value of a discrete bivariate function -

let's suppose have function f(x,y) , 2 vectors x , y, , want 2 find combination of values x , y gives maximum value of f .

*the function defined , bounded. x , y have approximately 1000 elements each.

*the function continuous, need highest point vector x , y though maximum might somewhere in between.

one possible implementation use 2 nested loops such in example; each x , y 10-element vectors , z=f(x,y)=x+y

max =-1  (x in 1:10){    (y in 2:20){        z = x+y        if (z>max){            z=max            x_sol = x            y_sol = y        }    } } x_sol #10 y_sol #20 

this code shows maximum value possible combinations of x , y when (x,y)=(10,20). code fine; problem when x , y hold more values, z more complex, , procedure has run hundreds of times, it's slow. wondering if there more elegant method replaces nested loop.

if want use brute-force approach optimization, vectorization fastest way achieve trying do:

x <- 1:100 y <- 1:100  df <- expand.grid(x=x,y=y)  df$z <- df$x + df$y  max(df$z) 

this solution of course depends on kind of function want use.