# source the function "constrOptim.nl"
source("g:/computing/constrOptim2.txt")
################################
fr <- function(x) { ## Rosenbrock Banana function 
x1 <- x[1] 
x2 <- x[2] 
100 * (x2 - x1 * x1)^2 + (1 - x1)^2 
} 
grr <- function(x) { ## Gradient of 'fr' 
x1 <- x[1] 
x2 <- x[2] 
c(-400 * x1 * (x2 - x1 * x1) - 2 * (1 - x1), 200 * (x2 - x1 * x1)) 
} 

constrOptim(c(.5,0), fr, grr, ui=rbind(c(-1,0),c(1,-1)), ci=c(-0.9,0.1)) 

# Note the difference in function and gradient counts 
# Also, the number of outer iterations are smaller because of 
# a different (and better) termination criterion
constrOptim2(c(.5,0), fr, grr, ui=rbind(c(-1,0),c(1,-1)), ci=c(-0.9,0.1)) 

################################
# Now we demonstrate the "bug" in constrOptim when maximizing, i.e. when control$fnscale = -1

fr.neg <- function(x) { ## negative Rosenbrock Banana function 
x1 <- x[1] 
x2 <- x[2] 
-(100 * (x2 - x1 * x1)^2 + (1 - x1)^2 )
} 
grr.neg <- function(x) { ## Gradient of 'fr.neg' 
x1 <- x[1] 
x2 <- x[2] 
-c(-400 * x1 * (x2 - x1 * x1) - 2 * (1 - x1), 200 * (x2 - x1 * x1)) 
} 

# This performs only one outer iteration 
constrOptim(c(.5,0), fr.neg, grr.neg, ui=rbind(c(-1,0),c(1,-1)), ci=c(-0.9,0.1), control=list(fnscale=-1)) 

# This correctly performs many outer iterations until convergence 
constrOptim2(c(.5,0), fr.neg, grr.neg, ui=rbind(c(-1,0),c(1,-1)), ci=c(-0.9,0.1), control=list(fnscale=-1)) 

################################
# Now we demonstrate the use of numerical gradient
fr <- function(x) { ## Rosenbrock Banana function 
x1 <- x[1] 
x2 <- x[2] 
100 * (x2 - x1 * x1)^2 + (1 - x1)^2 
} 
grr <- function(x) { ## Gradient of 'fr' 
x1 <- x[1] 
x2 <- x[2] 
c(-400 * x1 * (x2 - x1 * x1) - 2 * (1 - x1), 200 * (x2 - x1 * x1)) 
} 

# Nelder-Mead is used when gradient is not specified 
constrOptim(c(.5,0), fr, gr=NULL, ui=rbind(c(-1,0),c(1,-1)), ci=c(-0.9,0.1)) 

# BFGS algorithm is used even though gradient is not specified
constrOptim2(c(.5,0), fr, ui=rbind(c(-1,0),c(1,-1)), ci=c(-0.9,0.1))