bv_cvxbook_extra_exercises

Bv_cvxbook_extra_exercises

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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.

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