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Unformatted text preview: b â‰¥ 0, also Ëœ A Ëœ x = ( A,I ) Â· p x Axb P = AxAx + b = b Therefore Ëœ x is a solution of LP S . Â±or these it follows that: c T x = c T x + 0 T Â· ( Axb ) = ( c T , T ) Â· p x Axb P = Ëœ c T Ëœ x 2 2. Let LP S be given as min c T x s.t. x â‰¥ , Ax = b . Then with Ëœ A := p AA P , Ëœ b := p bb P , Ëœ c := c, Ëœ x := x we can describe an optimization problem in canonical form ( LP K ) by: min Ëœ c T Ëœ x s.t. Ëœ x â‰¥ , Ëœ A Ëœ x â‰¥ b From these it follows: x is exactly the feasible solution for LP S when x is a feasible solution for LP K . Furthermore, it follows that c T x = Ëœ c T Ëœ x . The proof concerning this is similar to the Â±rst case....
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This note was uploaded on 11/03/2009 for the course CS CS 149 taught by Professor Meinolf during the Spring '09 term at SanfordBrown College.
 Spring '09
 Meinolf

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