A far better model uses an extra constant term in the

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Unformatted text preview: −∆xT ∇f (x). You don’t really need nt λ for anything; you can work with λ2 instead. (This is important for reasons described below.) • There can be small numerical errors in the Newton step ∆xnt that you compute. When x is nearly optimal, the computed value of λ2 , i.e., λ2 = −∆xT ∇f (x), can actually be nt (slightly) negative. If you take the squareroot to get λ, you’ll get a complex number, and you’ll never recover. Moreover, your line search will never exit. However, this only happens when x is nearly optimal. So if you exit on the condition λ2 /2 ≤ 10−6 , everything will be fine, even when the computed value of λ2 is negative. • For the line search, you must first multiply the step size t by β until x + t∆xnt is feasible (i.e., strictly positive). If you don’t, when you evaluate f you’ll be taking the logarithm of negative numbers, and you’ll never recover. (b) LP solver with strictly feasible starting point. Using the centering code from part (a), implement a barrier method to solve the standard form LP mini...
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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.

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