bv_cvxbook_extra_exercises

# the resistance of the wires is given by ri li wi

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Unformatted text preview: the original LP is strictly feasible if and only if t⋆ &lt; 1, where t⋆ is the optimal value of the phase I problem. We can initialize x and t for the phase I problem with any x0 satisfying Ax0 = b, and t0 = 2 − mini x0 . (Here we can assume that min x0 ≤ 0; otherwise x0 is already a strictly i i feasible point, and we are done.) You can use a change of variable z = x +(t − 1)1 to transform the phase I problem into the form in part (b). Check your LP solver against cvx on several numerical examples, including both feasible and infeasible instances. 9.6 Barrier method for LP. Consider a standard form LP and its dual minimize cT x subject to Ax = b x0 maximize bT y subject to AT y c, with A ∈ Rm×n and rank(A) = m. In the barrier method the (feasible) Newton method is applied to the equality constrained problem minimize tcT x + φ(x) subject to Ax = b, where t &gt; 0 and φ(x) = − n i=1 log xi . The Newton equation at a strictly feasible x is given by ˆ ∇2 φ(ˆ) AT x A 0...
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