Chemical Engineering Hand Written_Notes_Part_107

Chemical Engineering Hand Written_Notes_Part_107 - 216...

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216 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES (9.57) α 0 = || g (1) || 2 || g (0) || 2 = || f ( x 1 ) || 2 || f ( x 0 ) || 2 Continuing the process, we form next direction as (9.58) s (2) = g (2) + α 0 s (0) + α 1 s (1) we want to choose α 0 and α 1 such that [ s (2) ] T As (0) =0 and [ s (2) ] T As (1) =0 (9.59) [ g (2) + α 0 s (0) + α 1 s (1) ] T As (0) =0 (9.60) g (2) A s (0) + α 1 [ s (2) ] T As (0) =0 (9.61) α 1 = ( g (2) ) T As (0) [ s (0) ] T As (0) = ( g (2) ) T A z (1) [ s (1) ] T As (1) (9.62) ( g (2) ) T [ g (1) g (0) ] g (0) Ag (0) = ( g (2) ) T I (1) [ s (1) ] T As (1) Continuing this process leads to the following general iteration scheme (9.63) s ( k ) = g ( k ) + || g ( k ) || 2 || g ( k 1) || 2 ¸ s ( k +1) These are called Fletcher and Reev’s iterations . For quadratic Φ ( z ) , the min- imumreachedinmax imum n steps. For non-quadratic Φ ( z ) , additional line searches and steps may be required.
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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_107 - 216...

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