Recently, I am studying a maximum-entropy problem. The problem is converted to the minimization of the following function

where v_i\in \mathbb{R}, \lambda\ge 0, c is a known constant, \mathbf{a} is a known vector, \mathcal{Z} denotes a known zonotope region, and the multivariate function f is the pointwise maximum of several affine functions.

How can I solve this problem with some commonly-used tool? Is it necessary to design algorithm on my own?