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Unformatted text preview: mize cT x
subject to Ax = b, x 0, with variable x ∈ Rn , given a strictly feasible starting point x0 . Your LP solver should take
as argument A, b, c, and x0 , and return x⋆ .
You can terminate your barrier method when the duality gap, as measured by n/t, is smaller
than 10−3 . (If you make the tolerance much smaller, you might run into some numerical trouble.) Check your LP solver against the solution found by cvx, for several problem instances.
The comments in part (a) on how to generate random data hold here too.
Experiment with the parameter µ to see the eﬀect on the number of Newton steps per centering
step, and the total number of Newton steps required to solve the problem.
Plot the progress of the algorithm, for a problem instance with n = 500 and m = 100, showing
duality gap (on a log scale) on the vertical axis, versus the cumulative total number of Newton
steps (on a linear scale) on the horizontal axis.
82 Your algorithm should return a 2 × k matrix history, (where k is the total number of centering
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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
- The Aeneid