Papers › On the optimal objective value of random linear programs
On the optimal objective value of random linear programs
Marzieh Bakhshi, James Ostrowski, Konstantin Tikhomirov
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We consider the problem of maximizing ⟨c,x ⟩ subject to the constraints Ax ≤1, where x∈Rⁿ, A is an m×n matrix with mutually independent centered subgaussian entries of unit variance, and c is a cost vector of unit Euclidean length. In the asymptotic regime n→∞, m/n→∞, and under some mild assumptions on c, we prove that the optimal objective value z^* of the linear program satisfies lim_(n→∞)√(2log(m/n)) z^*= 1 . We provide numerical experiments as supporting data for the theoretical predictions. Further, we carry out numerical studies of the limiting distribution and the standard deviation of z^*.
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