testFunOptimization2d {RCEIM}

2D test problem for RCEIM

Description

A two-dimensional problem for testing optimization methods.

This function was created for demonstrating the RCEIM package. It has the form:

f(x_1,x_2) = ((x_1-4)^2 + (x_2+2)^2)/50 - ((x_1+2)^2 + (x_2+4)^2)/90 -exp(-(x_1-2)^2) - 0.9*exp(-(x_2+2)^2) - 0.5*sin(8*x_1) - 0.25*cos(2*x_2) +0.25*sin(x_1*x_2/2) + 0.5*cos(x_2*x_1/2.5)

Usage

testFunOptimization2d(x)

Arguments

x

a vector with the point where the function is computed.

Value

The value of the function at the requested point (x_1, x_2).

Author(s)

Alberto Krone-Martins

See Also

testFunOptimization

Examples

# Create a graphical representation of the problem with a contour plot
dev.new()
xx <- seq(-10,10,by=0.1)
yy <- seq(-10,10,by=0.1)
zz <- matrix(nrow=length(yy), ncol=length(xx))
for(i in 1:length(xx)){
	for(j in 1:length(yy)){
		zz[i,j] <- testFunOptimization2d( c(xx[i],yy[j]) )
	}
}
image(xx,yy,zz, col=gray((50:100)/100), xlab="x", ylab="y")
contour(xx,yy,zz, add=TRUE)
rm(list=c('xx','yy','zz'))