util-projection: Projection of a point on a set

In GNE: Computation of Generalized Nash Equilibria

Projection of a point on a set

Description

Projection of a point z on the set defined by the constraints g(x) <= 0.

Usage

projector(z, g, jacg, bounds=c(0, 10), echo=FALSE, ...)

Arguments

z	The point to project.
g	The constraint function.
jacg	The jacobian of the constraint function.
bounds	bounds for the randomized initial iterate.
echo	a logical to plot traces.
...	further arguments to pass to g function.

Details

Find a point x in the set K which minimizes the Euclidean distance ||z - x||^2, where the set K is x, g(x) <= 0. The Optimization is carried out by the constrOptim.nl function of the package alabama.

Value

A vector x.

Author(s)

Christophe Dutang

See Also

See also GNE.

Examples

# 1. the rectangle set
#

g <- function(x)
	c(x - 3, 1 - x)

jacg <- function(x)
	rbind(
	diag( rep(1, length(x)) ),
	diag( rep(-1, length(x)) )
	)

z <- runif(2, 3, 4)

#computation
projz <- projector(z, g, jacg)

#plot
plot(c(1, 3), c(1, 1), xlim=c(0, 4), ylim=c(0,4), type="l", col="blue")
lines(c(3, 3), c(1, 3), col="blue")
lines(c(3, 1), c(3, 3), col="blue")
lines(c(1, 1), c(3, 1), col="blue")

points(z[1], z[2], col="red")
points(projz[1], projz[2], col="red", pch="+")

z <- runif(2) + c(1, 0)
projz <- projector(z, g, jacg)

points(z[1], z[2], col="green")
points(projz[1], projz[2], col="green", pch="+")



# 2. the circle set
#

g <- function(x) sum((x-2)^2)-1
jacg <- function(x) as.matrix( 2*(x-2) )

z <- runif(2) + c(1, 0)

#computation
projz <- projector(z, g, jacg)

#plot
plot(c(1, 3), c(1, 1), xlim=c(0, 4), ylim=c(0,4), type="n", col="blue")
symbols(2, 2, circles=1, fg="blue", add=TRUE, inches=FALSE)

points(z[1], z[2], col="red")
points(projz[1], projz[2], col="red", pch="+")

z <- c(runif(1, 3, 4), runif(1, 1, 2))
projz <- projector(z, g, jacg)

points(z[1], z[2], col="green")
points(projz[1], projz[2], col="green", pch="+")

GNE documentation built on March 31, 2023, 9:25 p.m.