?optim

# The default method for optim() is called "Nelder-Mead" optimization

optim(par=c(0,0),fn=my.fcn,control=list(fnscale=-1))

# "SANN" does simulated annealing

optim(par=c(0,0),fn=my.fcn,control=list(fnscale=-1,maxit=100000),method="SANN")

# "CG" is a gradient method (Note: "BFGS" is another gradient method)

optim(par=c(0,0),fn=my.fcn,control=list(fnscale=-1,maxit=10000),method="CG")

optim(par=c(-2,-2),fn=my.fcn,control=list(fnscale=-1,maxit=10000),method="CG")

## The tricky function of one variable:

# "Nelder-Mead" optimization:

optim(par=c(0),fn=my.fcn.simp,control=list(fnscale=-1))

# It doesn't work here ... R recommends 'optimize'...

# optimize() does simple one-dimensional optimization (but not always well ... see below)

?optimize

# By default, 'optimize' will do minimization, so set maximum=T if you want the maximum.
optimize(my.fcn.simp, lower=-512, upper=512, maximum=T)

# It didn't work --- it found a local maximum, not the global maximum.
# The Simple Stochastic Search method was slower but better in this case.