smooth minimization of piecewise linear convex function

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.