R Programming/Optimization

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Numerical Methods[edit]

One dimensional problem[edit]

The one dimensional problem :

> func <- function(x){
+ 	return ( (x-2)^2 )
+ 	}
> (func(-2))
[1] 16
>
> # plot your function using the 'curve function'
> curve(func,-4,8) 
>
> # Here is another way to plot the function
> # using a grid
> grid <- seq(-10,10,by=.1) 
> func(grid)
> plot(grid,func(grid))
> 
> # you can find the minimum using the optimize function
> optimize(f=func,interval=c(-10,10))
$minimum
[1] 2
 
$objective
[1] 0

Newton-Raphson[edit]

  • nlm() provides a Newton algorithm.
  • maxLik package for maximization of a likelihood function. This package includes the Newton Raphson method.
  • newtonraphson() in the spuRs package.

BFGS[edit]


> func <- function(x){
+ 	out <- (x[1]-2)^2 + (x[2]-1)^2
+ 	return <- out
+ 	}> 
> optim(par=c(0,0), fn=func, gr = NULL,
+       method = c("BFGS"),
+       lower = -Inf, upper = Inf,
+       control = list(), hessian = T)
> optim(par=c(0,0), fn=func, gr = NULL,
+       method = c("L-BFGS-B"),
+       lower = -Inf, upper = Inf,
+       control = list(), hessian = T)

Conjugate gradient method[edit]

  • optim() with method="cg".

Trust Region Method[edit]

  • "trust" package for trust region method


The Nelder-Mead simplex method[edit]

> func <- function(x){
+ 	out <- (x[1]-2)^2 + (x[2]-1)^2
+ 	return <- out
+ 	}
> 
> optim(par=c(0,0), fn=func, gr = NULL,
+       method = c("Nelder-Mead"),
+       lower = -Inf, upper = Inf,
+       control = list(), hessian = T)


  • The boot package includes another simplex method

Simulation methods[edit]

Simulated Annealing[edit]

  • The Simulated Annealing is an algorithm which is useful to maximise non-smooth functions. It is pre implemented in optim().
> func <- function(x){
+ 	out <- (x[1]-2)^2 + (x[2]-1)^2
+ 	return <- out
+ 	}> 
> optim(par=c(0,0), fn=func, gr = NULL,
+       method = c("SANN"),
+       lower = -Inf, upper = Inf,
+       control = list(), hessian = T)

EM Algorithm[edit]

Genetic Algorithm[edit]

  • rgenoud package for genetic algorithm[3]
  • gaoptim package for genetic algorithm[4]

References[edit]

  • Venables and Ripley, Chapter 16.
  • Cameron and Trivedi, Microeconometrics, chapter 10
  • Braun and Murdoch (Chapter 7)[5] is a very good reference on optimization using R.
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