optimization problem in R ... can this be done?

Spencer: Thank you for the helpful suggestions. I have another
question following some code I wrote. The function below gives a
crude approximation for the x of interest (that value of x such that
g(x,n) is less than 0 for all n).

# // btilda optimize g(n,x) for some fixed x, and then approximately
finds that g(n,x) #    such that abs(g(n*,x)=0 // btilda <-
function(range,len) { # range: over which to look for x bb <-
seq(range[1],range[2],length=len) OBJ <- sapply(bb,function(x) {fixed
<- c(x,1000000,692,500000,1600,v1,217227);
return(optimize(g,c(1,1000),maximum=TRUE,tol=0.0000001,x=fixed)$objective)})
 tt <- data.frame(b=bb,obj=OBJ) tt$absobj <- abs(tt$obj) d <-
tt[order(tt$absobj),][1:3,] return(as.vector(d)) }

For instance a run of

btilda(c(20.55806,20.55816),10000) .... returns:

b                  obj                    absobj 5834   20.55812
-0.0004942848    0.0004942848 5833   20.55812     0.0011715433
0.0011715433 5835   20.55812    -0.0021601140    0.0021601140

My question is how to improve the precision of b (which is x) here.
It seems that seq(20.55806,20.55816,length=10000 ) is only precise to
5 or so digits, and thus, is equivalent for numerous succesive

values. How can I get around this?


Spencer Graves <spencer.graves at pdf.com> wrote: Part of the R culture
is a statement by Simon Blomberg immortalized in library(fortunes)
as, "This is R. There is no if. Only how."

I can't see now how I would automate a complete solution to your 
problem in general. However, given a specific g(x, n), I would start
by writing a function to use "expand.grid" and "contour" to make a
contour plot of g(x, n) over specified ranges for x = seq(0, x.max,
length=npts) and n = seq(0, n.max, npts) for a specified number of
points npts. Then I'd play with x.max, n.max, and npts until I got
what I wanted. With the right choices for x.max, n.max, and npts, the
solution will be obvious from the plot. In some cases, nothing more
will be required.

If I wanted more than that, I would need to exploit further some 
specifics of the problem. For that, permit me to restate some of what
I think I understood of your specific problem:

(1) For fixed n, g(x, n) is monotonically decreasing in x>0.

(2) For fixed x, g(x, n) has only two local maxima, one at n=0 (or 
n=eps>0, esp arbitrarily small) and the other at n2(x), say, with a 
local minimum in between at n1(x), say.

With this, I would write functions to find n1(x) and n2(x) given x. I
might not even need n1(x) if I could figure out how to obtain n2(x) 
without it. Then I'd make a plot with two lines (using "plot" and 
"lines") of g(x, 0) and g(x, n2(x)) vs. x.

By the time I'd done all that, if I still needed more, I'd probably 
have ideas about what else to do.

hope this helps. spencer graves


Gregory Gentlemen wrote:

Im trying to ascertain whether or not the facilities of R are
sufficient for solving an optimization problem I've come accross.
Because of my limited experience with R, I would greatly appreciate
some feedback from more frequent users. The problem can be
delineated as such:

A utility function, we shall call g is a function of x, n ...
g(x,n). g has the properties: n > 0, x lies on the real line. g may
take values along the real line. g is such that g(x,n)=g(-x,n). g
is a decreasing function of x for any n; for fixed x, g(x,n) is
smooth and intially decreases upon reaching an inflection point,
thereafter increasing until it reaches a maxima and then declinces
(neither concave nor convex).

My optimization problem is to find the largest positive x such that
g(x,n) is less than zero for all n. In fact, because of the
symmetry of g around x, we need only consider x > 0. Such an x does
exists in this problem, and of course g obtains a maximum value of
0 at some n for this value of x. my issue is writing some code to
systematically obtain this value.

Is R capable of handling such a problem? (i.e. through some sort of
optimization fucntion, or some sort of grid search with the
relevant constraints)

Any suggestions would be appreciated.

Gregory Gentlemen gregory_gentlemen at yahoo.ca



The following is a sketch of an optimization problem I need to
solve.