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Unformatted text preview: m n matrix A of rank m . If Z T Zv = 0, then Zv = 0. (p. 432) [* means omit] 10. or the problem Min f ( x ) subject to Ax = b and Z a basis null space matrix for A , let ( v ) = f ( x + Zv ), then ( v ) = Z T f ( x ) and 2 ( v ) = Z T 2 f ( x ) Z . (p. 429) 11. or the problem Min f ( x ) subject to Ax = b and Z the null space matrix of A , let ( v ) = f ( x + Zv ), then ( v ) = 0 if and only if Z T f ( x ) = 0 if and only if f ( x ) = A T for some vector . (p. 431) 12. or the problem Min f ( x ) subject to Ax b , suppose that x * is a stationary point of ( v ) = f ( x + Zv ) such that f ( x * ) = A T * for A the submatrix of A of active constraints for x * . If * 1 < 0, then x * is not a local minimizer. (p. 440) 1 . 2...
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- Spring '10
- Linear Programming