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Unformatted text preview: I chose pattern search because it has proven convergence and does not require derivatives of F with respect to x . Note that these derivatives are not available for this problem: we can compute derivatives of y with respect to t but not with respect to x . And since our value of y (1) is only an approximation, the use of Fnite dierences to estimate derivatives with respect to x would yield values too noisy to be useful. CHALLENGE 9.13. Method conv. rate Storage f evals/itn g evals/itn H evals/itn Truncated Newton > 1 O ( n ) n + 1 Newton 2 O ( n 2 ) 1 1 1 Quasi-Newton > 1 2 O ( n 2 ) 1 1 steepest descent 1 O ( n ) 1 1 Conjugate gradients 1 O ( n ) 1 1 Notes on the table: 1. Once the counts for the linesearch are omitted, no function evaluations are needed. 2. or a single step, Quasi-Newton is superlinear; it is n-step quadratic....
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- Fall '11