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Define a functional space of functions of the form $F(t)=p_1 exp^{-\mu_1(\delta-t)}+p'_1 (1-exp^{-\mu_1(\delta-t)}))$. $p_1,p'_1,\delta,\mu$ are parameters in [0,1] and trivially, variation of these parameters builds the instances of our functional space. The goal is to solve the following optimization problem tractably:

$max_{F_1,F_2\in F(t)} \int_0^\delta \lambda exp^{-\lambda t} (F_1(t)-F_2(t))dt$.

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This is some strange notation ($F_1,F_2\in F(t)$?). Why don't you just do the integral so you end up with a finite-dimensional problem and then optimize? Voting to close. –  Noah Stein Mar 6 '13 at 13:51
    
You know the general forms of $F_1$ and $F_2$ functions. How do you integrate over unknown instances of the functional space? –  Star Mar 6 '13 at 15:05
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