[R-SIG-Finance] Quadratic Optimization Problem: Kelly Criterion

[Andrew O]

I'm trying to do a kelly criterion optimization of a group of simultaneous 
binary bets.  Each bet has two values associated with it, the probability of 
success, P, and the payout if successful, r.  If the bet loses, the entire 
premium is lost.

So if I put in a set of 20 bets that need to be bet on simultaneously, what 
is the ideal weighting, X, to give to each to maximize the growth of capital 
from placing those bets.  This is obviously more difficult than the trivial 
calculation of figuring out the highest expected value(all capital invested 
in the bet with the most profitable bet).

A paper, "Algorithms for optimal allocation of bets on many
simultaneous events", gives a more detailed description of the problem here: 
http://www.filedropper.com/whitrow2007kellypaper

For me, the limitations on the calculation are that all values for X must be 
positive (long only) and the sum of all the X must be less than or equal to  
1 (no leverage).

Are there any packages or methods that would be useful for solving this kind 
of problem?