Differential Equations Solutions 81

Differential Equations Solutions 81 - 91(a Given any e f...

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91 (a) Given any Δ b e f ,let ¯ σ 1 ¯ σ 2 ¯ σ 3 = ¯ ¯ ¯ ¯ ¯ ¯ FK + E D 0 0 λ I · Δ b e Δ f ¸ + r D b e λ f ¯ ¯ ¯ ¯ ¯ ¯ . Then Δ b e f , ¯ σ 1 , ¯ σ 2 ,and ¯ σ 3 form a feasible solution to the linear programming problem, and ¯ σ = m X i =1 ¯ σ 1 i + q X i =1 ¯ σ 2 i + n X i =1 ¯ σ 3 i = ° ° ° ° · FK + E D 0 ¸· Δ b e Δ f ¸ + · r D b e ¸ ° ° ° ° p . Therefore, a solution to the linear programming problem minimizes the norm, and a minimizer of the norm is a solution to the linear programming problem, so the two are equivalent. (b) By similar reasoning, we obtain min Δ b e , Δ f , ¯ σ ¯ σ subject to ¯ σ 1 F Δ b e +( K + E f r ¯ σ 1 ¯ σ 1 D Δ b e + D b e ¯ σ 1 ¯ σ 3 1 λ Δ f + λ f ¯ σ 3 1 where 1 is a column vector with each entry equal to 1, and of dimension m in the Frst two inequalities, q in the second two, and n in the last two. CHALLENGE 15.6. See the MATLAB program posted on the website.
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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