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

[Spencer Graves]

	  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.
> 
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-- 
Spencer Graves, PhD
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