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Operations research, linear programming, control theory, systems theory, optimal control, game theory

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Has the following generalization of monotropic programming been studied in the literature?

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. …
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