Unformatted text preview: Î» . Then the optimality conditions are Is + A T Î» = c , s â‰¥ , x â‰¥ , Ax = b , s T x = 0 . The central path: Ax = b , A âˆ— w + s = c , Î¼ X âˆ’ 1 e + s = , where s , x â‰¥ 0 (since the feasible cone is the positive orthant). Both sets of conditions have Ax = b . Setting Î» = w shows the equivalence of s + A T Î» = c and A âˆ— w + s = c , since A âˆ— = A T . Multiplying Î¼ X âˆ’ 1 e + s = by X , we obtain Î¼ e + Xs = , which is equivalent to s T x = 0 when Î¼ = 0, since x and s are nonnegative. Therefore the conditions are equivalent....
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- Fall '11
- Optimization, Equivalence relation, Binary relation, Constraint satisfaction