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Unformatted text preview: method (and has be rediscovered many times): Input: f , ∇ f , x , α > , < c 1 < 1 , search direction p Output: α where f ( x + s p ) ≤ f ( x ) + c 1 α p T ∇ f ( x ) α ← α while f ( x + α p ) > f ( x ) + c 1 α p T ∇ f ( x ) α ← α / 2 end while 1 Show that this algorithm terminates in ﬁnite time provided p T ∇ f ( x ) < and f is at least once continuously differentiable. 4. Many programmers implementing a line search algorithm like the Goldstein/Armijo line search might use the condition while f ( x + α p ) ≥ f ( x ) ... If we use x + α p with p =∇ f ( x ) for the new value of x after each line search, this method might not converge to a critical point. Can you explain why? 2...
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 Spring '12
 DavidStewart
 Derivative, Optimization, pseudocode, steepest descent algorithm, Goldstein/Armijo line search, iteration count kmax

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