Smoothed analysis is a method for analyzing the performance of algorithms, used especially for those algorithms whose running time in practice is significantly better than what can be proven through w...

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Let $\mathcal{P}$ be the following primal optimization problem \begin{align} \mathcal{P}: \text{minimize}_x \quad & f_0(x)\\ \text{subject to} \quad & f_i(x) \leq 0, \quad i = 1, ..., m \\ ...