I am interested in problems of the form

$$\min_{x \in C} \sum_{i=1}^n\sum_{j=1}^n f(x_i,x_j)$$

where $C$ is a convex subset of $\mathbb{R}^{n}$, and $f \colon \mathbb{R}^{2} \to \mathbb{R}$ is convex.

Question: Has this class of optimization problems being studied in some detail?

Thank you in advance for your help.