Before revision:  We prove that finding the optimal advertising strategy is hard, even in the simple case that the buyer typeis known. Nevertheless, we show that when the buyer type is known, the problem is equivalent to finding the concave closure of a function  . Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve  the optimal mechanism by a convex program ( with exponential size in general, polynomial size for special cases).
After revision:  We study the problem in two settings. 1. The seller targets the buyers of a certain type. In this case, we prove that finding the optimal advertising strategy is equivalent to finding the concave closure of a function . Based on this observation, we prove some properties of the optimal mechanism, which allow us to solve the optimal mechanism by a convex program ( with exponential size in general, polynomial size for special cases).