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Table 2 Summary of the main complexity results for PCDM established in this paper

From: Parallel coordinate descent methods for big data optimization

Setting Complexity Theorem
Convex \(f\) \(\mathcal{O} \left( \frac{\beta n}{{{\mathrm{\mathbf {E}}}}[|\hat{S}|] }\frac{1}{\epsilon }\log \left( \tfrac{1}{\rho }\right) \right) \) 17
\(\begin{array}{l} \hbox {Strongly convex} f \mu _f(w)+\mu _\Omega (w)>0 \end{array}\) \(\frac{n}{{{\mathrm{\mathbf {E}}}}[|\hat{S}|]} \frac{\beta + \mu _\Omega (w)}{\mu _f(w)+\mu _\Omega (w)} \log \left( \frac{F(x_0)-F^*}{\epsilon \rho }\right) \) 18