Assignment9Solution - Fall 2010 Optimization I (ORIE...

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Unformatted text preview: Fall 2010 Optimization I (ORIE 3300/5300) Assignment 9 Solution Problem 1 (a) Model file: #hw9.mod param m; param n; param A {1..m, 1..n}; param b {1..m}; param c {1..n}; var x {1..n}; maximize objective: sum{j in 1..n} c[j]*x[j]; subject to constraint: sum{j in 1..n} A[1, j]*x[j] <=b[1]; subject to constrainteq {i in 2..m}: sum{j in 1..n} A[i, j]*x[j] = b[i]; subject to nonnegativity {j in 2..n} : x[j] >= 0; Data file: #hw9.dat param m = 3; param n = 5; param A: 1 2 3 4 5:= 1 -1 3 -2 4 2 2 -2 -1 3 2 1 3 3 -1 2 -2 -3; param b:= 1 10 2 6 3 -7; param c:= 1 11 2 -3 3 2 4 -8 5 -12; 1 Fall 2010 Optimization I (ORIE 3300/5300) Output: ampl: reset; model hw9.mod; data hw9.dat; solve; MINOS 5.5: optimal solution found. 2 iterations, objective -27 ampl: display x; x [*] := 1-1 2 3 4 2 5 ; (b) The dual problem: min 10 y 1 + 6 y 2- 7 y 3 s.t.- y 1- 2 y 2 + 3 y 3 = 11 3 y 1- y 2- y 3 ≥- 3- 2 y 1 + 3 y 2 + 2 y 3 ≥ 2 4 y 1 + 2 y 2- 2 y 3 ≥- 8 2 y 1 + y 2- 3 y 3 ≥ - 12 y 1 ≥ y 2 , y 3 free .....
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This note was uploaded on 01/25/2011 for the course ORIE 5300 taught by Professor Todd during the Fall '08 term at Cornell University (Engineering School).

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Assignment9Solution - Fall 2010 Optimization I (ORIE...

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