bv_cvxbook_extra_exercises

# Bv_cvxbook_extra_exercises

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online