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

From: Gregory Gentlemen <gregory_gentlemen_at_yahoo.ca>
Date: Sat 25 Jun 2005 - 13:58:42 EST

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

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

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