bv_cvxbook_extra_exercises

the resistance of the wires is given by ri li wi

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: the original LP is strictly feasible if and only if t⋆ < 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 > 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...
View Full Document

Ask a homework question - tutors are online