Introduction to Semidefinite Programming
We will write the standard linear programming dual problem as: m LD : maximize y ib i i=1 m s.t. y ia i + s = c i=1 n s ∈ℜ +. Given a feasible solution x of LP and a feasible solution (y,s) of LD, the duality gap is simply c x− P m i=1 y ib i = (c− P m · i=1 y ia i)·x = s·x ≥ 0, because x ≥ 0 and s ≥ 0.
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