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Unformatted text preview: e ﬁrst row contains the number of Newton steps required for each centering step,
and whose second row shows the duality gap at the end of each centering step. In order to
get a plot that looks like the ones in the book (e.g., ﬁgure 11.4, page 572), you should use the
following code:
[xx, yy] = stairs(cumsum(history(1,:)),history(2,:));
semilogy(xx,yy);
(c) LP solver. Using the code from part (b), implement a general standard form LP solver, that
takes arguments A, b, c, determines (strict) feasibility, and returns an optimal point if the
problem is (strictly) feasible.
You will need to implement a phase I method, that determines whether the problem is strictly
feasible, and if so, ﬁnds a strictly feasible point, which can then be fed to the code from
part (b). In fact, you can use the code from part (b) to implement the phase I method.
To ﬁnd a strictly feasible initial point x0 , we solve the phase I problem
minimize t
subject to Ax = b
x ( 1 − t ) 1, t ≥ 0, with variables x and t. If we can ﬁnd a feasible (x, t), with t < 1, then x is strictly feasible for
the original problem. The converse is also true, so...
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 Fall '13
 F.Borrelli
 The Aeneid

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