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Is it possible to apply Nesterov's smooth minimization of non smooth function on a problem of the form

$$\mathop {\min }\limits_{\lambda \in {R^m}} \mathop {\max }\limits_{\sigma \in {{\left\{ {0,1} \right\}}^n}} a_\sigma ^T\lambda $$

where we have an oracle to calculate

$$f(\lambda ) = \mathop {\max }\limits_{\sigma \in {{\left\{ {0,1} \right\}}^n}} a_\sigma ^T\lambda $$

and

$$\partial f\left( \lambda \right)$$

further, $a_\sigma ^T$ is a (-1,0,1) vector depending on ${\sigma \in {{\left\{ {0,1} \right\}}^n}}$

Thank you.

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No, I think to apply Nesterov's smoothing technique you need access to a more powerful oracle, namely to a projection oracle not just the linear oracle that you have.

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