Minimize the minimum - Linear programming Consider an optimization problem with variables $x_1, x_2, \dots, x_n \in \mathbb{R}$ (maybe subject to some linear constraints), and linear functions $\{f_i(x_1, \dots, x_n)\}_{1\leq i\leq m}$. We want to minimize $\min_{1\leq i\leq m} f_i(x_1, \dots, x_n)$. 
Is it possible to formulate this problem as a single linear programming one?
(Maybe it's trivial since everything is linear, I don't know. If it is, what about the same problem, except that every everything may not be linear and we want to formulate it as "$\min c^Tx$ s.t. [list of non-linear constraints]")

You can maximize a minimum or minimize a maximum with a single LP, but min-min and max-max are both non-convex.
