xn each with probability 1n the third function is

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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 worst-case 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 n-vectors that satisfy 1T c...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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