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Is there a straightforward way to formulate the following as a linear program, or something similarly amenable to easy solution? The problem is:
minimize $A \;\mathrm{vec}(U)$ over symmetric $n\times n$
matrices $U$ subject to $U_{i,j} \leq \max\{U_{i,k}, U_{k,j}\}$
for all $i,j,k$.
H...