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Unformatted text preview: why the optimal value of the
dual is f (x).
(c) Use the expression for f (x) found in part (b) in the original problem, to obtain a single LP
equivalent to the original robust LP.
(d) Carry out the method found in part (c) to solve a robust LP with data
rand(’seed’,0);
A = rand(30,10);
b = rand(30,1);
c_nom = 1+rand(10,1); % nominal c values and C described as follows. Each ci deviates no more than 25% from its nominal value, i.e.,
0.75cnom
c
1.25cnom , and the average of c does not deviate more than 10% from the
average of the nominal values, i.e., 0.9(1T cnom )/n ≤ 1T c/n ≤ 1.1(1T cnom )/n.
37 Compare the worstcase cost f (x) and the nominal cost cT x for x optimal for the robust
nom
problem, and for x optimal for the nominal problem (i.e., the case where C = {cnom }). Compare the values and make a brief comment.
4.22 Diagonal scaling with prescribed column and row sums. Let A be an n × n matrix with positive
entries, and let c and d be positive nvectors that satisfy 1T c...
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 Fall '13
 F.Borrelli
 The Aeneid

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