Consider the following: $\exists y^* \in R^m \setminus \{0\} $ such that:
$$ y^* ( f(x_0) - k_1) \leq a \leq y^*(f(x) + k_2) \ \forall x \in \mathbb R^n, \ k_1,k_2 \in K \subset \mathbb{R^m} \ f: \mathbb{R^n} \rightarrow \mathbb{R^m}$$
f is convex and K a convex cone.
Why can I write on the right side: $$y^*(f(x) + k_2) = y^*(f(x)) + y^*(k_2)$$