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Evolution and Optimum Seeking

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80 Hill climbing Strategies<br />

Step 2: (Forget second order information)<br />

Replace H (k) H (0) = I<br />

h (k)<br />

i h (0)<br />

i<br />

<strong>and</strong> v (k) ;g (k) :<br />

=1foralli = 1(1)n<br />

Step 3: (Line search <strong>and</strong> eventual break-o )<br />

Determine x (k+1) such that<br />

F (x (k+1) ) = min<br />

s fF (x (k) + sv (k) )g:<br />

If F (x (k+1) ) F (x (k) ), end the search with result x (k) <strong>and</strong> F (x (k) ).<br />

Step 4: (Prepare for inverse Hessian update)<br />

Determine g (k+1) by the above di erence scheme.<br />

Construct y (k) = x (k+1) ; x (k) <strong>and</strong> z (k) = g (k+1) ; g (k) :<br />

If k>n<strong>and</strong> v (k)<br />

i

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