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
[EMAIL PROTECTED]
The following is a sketch of an optimization problem I need to solve.
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