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An optimization problem with variables on the exponential of a complex number

$$\min_t \quad\quad\operatorname{Re} \sum\limits_{i = 1}^N {\left( {{e^{ - j2\pi {f_i}t}}{r_i}} \right)}, $$where $\operatorname{Re}$ refers to get the real part of a complex number, $\{f_i\}$ is an arithmetic progression with $i = 1,2,...,N$, ${r_i} \in \mathcal{Z}$ are with unequal modulus and angles.