C b the case where a is positive semidenite but

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Unformatted text preview: ts, to verify that your implementation gives asymptotic quadratic convergence. As stopping criterion, you can use λ2 /2 ≤ 10−6 . Experiment with varying the algorithm parameters α and β , observing the effect on the total number of Newton steps required, for a fixed problem instance. Check that your computed x⋆ and ν ⋆ (nearly) satisfy the KKT conditions. To generate some random problem data (i.e., A, b, c, x0 ), we recommend the following approach. First, generate A randomly. (You might want to check that it has full rank.) Then generate a random positive vector x0 , and take b = Ax0 . (This ensures that x0 is strictly feasible.) The parameter c can be chosen randomly. To be sure the sublevel sets are bounded, you can add a row to A with all positive elements. If you want to be able to repeat a run with the same problem data, be sure to set the state for the uniform and normal random number generators. Here are some hints that may be useful. • We recommend computing λ2 using the formula λ2 =...
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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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