optimizing function over x,y

Hello all,
 
 I would like to maximize or minimize a given math function over a
 specific set of values.
 
 I was checking out Wolfram Alpha (
 and it can do simple optimization problems in math, such as
 
      maximize 15*x - x**2 over 0 to 15
 
      (
 
 which finds the maximum value and input for x in the range 0 to 15.
 Very cool. (This is of course a very simple example).
 
 Reading the R documentation I found out that with R I can do this:
 
 
   f<-function(x) (15*x)-x**2
   optimize(f, c(0,15), lower=0,upper=15, maximum=TRUE)
 
 which works very nicely too!
 
 
 What I would like to do, but what Wolfram Alpha apparently can't do
 (according to a post in their community forum) is to maximize (or
 minimize) functions that contain two variables, x and y, or more. So
 for example a very simple example would be
 
     minimize x**2 + y**2 over x:0 to 15, y:0-12  -- this does not work
                                                  -- though I'm 
unclear about
                                                  -- the correct 
syntax too.
 
 Is there a way to do this in R in just a neat and easy way as R
 optimizes a 1-D function?
 
 For this particular instance I am interested in the minimum of
 
    x * sin(4*x) + 1.1 * sin(2*y), where x,y in range 0-10
 
 so an example of this in R would be great, though in other problems
 the range may not be identical for x and y.
 
 Thanks,
 
 Esmail
 
 ps: Has anyone written any programs in Python that they then have used
      to call R functions? I am thinking of writing some of my scripts 
in
      Python, but then accessing some of R's functions.
 

Look at nlminb() or optim(), in particular the option `method = "L-BFGS-B"' or the function spg() in "BB" package.

With these you can optimize over any number of variables.

Ravi.