bv_cvxbook_extra_exercises

# Each node of the tree is connected to some subcircuit

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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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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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