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Lecture-7 - Lecture-7 Step Length Selection Homework(Due...

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1 Lecture-7 Step Length Selection Homework (Due 2/20/01) • 3.1 • 3.2 • 3.5 • 3.6 • 3.7 3.9 • 3.10 Show equation 3.44 The last step in the proof of Theorem 3.6. (see slides)
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2 Sufficient condition ) 1 , 0 ( , ) ( ) ( 1 1 + + c p f c x f p x f k T k k k k a a ) 1 , 0 ( , ) ( ) ( 1 1 - + c p f c x f p x f k T k k k k a a The reduction should be proportional to both the step length, and directional derivative. St line ) 1 , 0 ( , ) ( ) ( 1 1 + + c p f c x f p x f k T k k k k a a ) ( ) ( a a l p x f k k + 4 1 10 - = c Sufficient condition ) ( ) ( a a l p x f k k + Problem: The sufficient decrease condition is satisfied for all small values of step length
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