Parametrized linear optimization problem
Submitted by Anonymous on Mon, 08/27/2007  15:29.
Let be L different probability distributions over M elements:
where , and.
Let be L real, positive constants. Let be a real positive constant, and let .
We have the following linear optimization problem:
Maximize
Such that:
 are M positive real variables;


We know that for some value of , the optimization problem accepts a solution with the maximum objective . I would like to know the minimum value of such that the problem still accepts a solution.
Thank you for your help.