calculus of variations type problem

Hi,

I have recently been thinking about an optimization problem to which I
can't find an easy solution. The problem is: find a C^3 function f :
[0,T] -> R which minimizes

\int_0^T (d^3f/dt^3)^2 dt

subject to the constraint

\sum_i exp(-f(t_i)) c_i

where the sum is over a finite set, and c_i are arbitrary real numbers.
obviously the problem is quite specific and can be translated into
various equivalent forms. However I haven't figured out a way to make
it amenable to the techniques I learnt as an undergrad, so if anyone
could advise me on an approach, that would be great.

Thanks,
David

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