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Unformatted text preview: . Then the optimality conditions are Is + A T = c , s , x , Ax = b , s T x = 0 . The central path: Ax = b , A w + s = c , X 1 e + s = , where s , x 0 (since the feasible cone is the positive orthant). Both sets of conditions have Ax = b . Setting = w shows the equivalence of s + A T = c and A w + s = c , since A = A T . Multiplying X 1 e + s = by X , we obtain e + Xs = , which is equivalent to s T x = 0 when = 0, since x and s are nonnegative. Therefore the conditions are equivalent....
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- Fall '11