I'm currently working on the following problem $$ \min_y \underset{(i,j) \in E}\max \left | \left \langle \tilde{a_{ij}},y \right \rangle \right | \quad \text{such that } \left \langle f,y \right \rangle = 1 $$
which i minimize using Nesterov's smoothing on the following reformulation : $$ \underset{y}{\min} \quad \mu \log \left( \sum_{(i,j)} e^{\frac{\left \langle \tilde{a_{ij}},y \right \rangle }{\mu}}+e^{-\frac{\left \langle \tilde{a_{ij}},y \right \rangle }{\mu}} \right) \quad \text{such that } \quad \begin{aligned}[t] & \left \langle f,y \right \rangle = 1 \end{aligned} $$ My question is the following, my algorithm uses first order method for which i need a stopping criterion, for which the dual gap seems to be the best choice, how would i go about determining the formulation of the gap? Thanks !