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Unformatted text preview: re than (U − L)suboptimal for the Boolean LP.
ˆ This rounding need not work; indeed, it can happen that for all threshold values, x is infeasible.
ˆ
But for some problem instances, it can work well. Of course, there are many variations on this simple scheme for (possibly) constructing a feasible,
good point from xrlx .
Finally, we get to the problem. Generate problem data using
rand(’state’,0);
n=100;
m=300;
A=rand(m,n);
b=A*ones(n,1)/2;
c=rand(n,1);
20 You can think of xi as a job we either accept or decline, and −ci as the (positive) revenue we
generate if we accept job i. We can think of Ax b as a set of limits on m resources. Aij , which
is positive, is the amount of resource i consumed if we accept job j ; bi , which is positive, is the
amount of resource i available.
Find a solution of the relaxed LP and examine its entries. Note the associated lower bound L.
Carry out threshold rounding for (say) 100 values of t, uniformly spaced over [0, 1]. For each value
of t, note the objective value cT x and the maximum constraint violati...
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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 University of California, Berkeley.
 Fall '13
 F.Borrelli
 The Aeneid

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