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Feb 4, 2019 at 7:47 comment added Dima Pasechnik yes it can happen, I suppose. But seems to be hard to quantify.
Feb 4, 2019 at 4:26 comment added Erel Segal-Halevi Indeed, in the small examples that I checked, replacing the term $a_ij x_i$ with the term $f_ij(xi)$, where $f_ij$ is concave and normalized ($f_ij(0)=0$), seems like "pumping a bit of air" from $P$, while keeping its vertices in their place. But is this always the case? Can't it happen that we "pump too much air" and destroy the structure of $P$?
Feb 3, 2019 at 11:49 history answered Dima Pasechnik CC BY-SA 4.0