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Unformatted text preview: (b) Let f ( x ) = 1 2 x T A T Ax − b T Ax . Show that solving ( OP ) is equivalent to minimizing f ( x ). What is ∇ f ( x )? (c) Given x and d , ±nd explicitly λ that solves: min λ f ( x + λd ) . (d) Formulate an algorithm that solves (OP) using steepest descent. What is the step size at each iteration? 1 6. (Steepest Descent) Implement the steepest descent algorithm to minimize (a) f ( x ) = 5 x 2 1 + x 2 2 + 4 x 1 x 2 − 14 x 1 − 6 x 2 + 20 as presented in class. Check your results with the handout. (b) f ( x ) = 1 2 x T Qx − c T x + 10 for (i) x = b 40 − 100 B , Q = b 20 5 5 2 B , c = b 14 6 B . (ii) x = b 40 − 100 B , Q = b 20 5 5 16 B , c = b 14 6 B . Set the stop criterion ε = 106 . Make the tables and Fgures as shown in the handout. Attach your Matlab code. 2...
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 Spring '09
 Optimization, Fermat's theorem, steepest descent

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