Getting an optimal decomposition is definitely an open problem. (And, of course, the decomposition is intractable, $\exp(n)$ gates for large $n$.) A "simpler" question you might ask first is what is the shortest sequence of cnots and single qubit rotations by any angle, (what IBM, Rigetti, and soon Google currently offer, this universal basis of gates can be expressed in terms of your basis of Cliffords and t-gates). This "simpler" question is also open and has a non-unique answer. A related question is what is an exact optimal decomposition of gates from a universal basis to go from ground state to a given final state.
I am assuming you are referring to exact decompositions. If you want approximate decompositions, there are different methods for that, such as the Trotter-Suzuki decomposition, or approximating an exact decomposition.
The "quantum csd compiler" in Qubiter does a non-optimized decomposition of any n qubit unitary into cnots and single qubit rots using the famous csd (Cosine-Sine Decomposition) subroutine from LAPACK. Some enterprising person could try to find optimizations for Qubiter's quantum compiler. You can use Qubiter's compiler, for example (I wrote a paper on this), to let your classical computer re-discover Coppersmith's quantum Fourier Transform decomposition!
Qubiter is open source and available at github (full disclosure - I wrote it).