lecture8 - lehigh-logo IE417: Nonlinear Programming:...

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Unformatted text preview: lehigh-logo IE417: Nonlinear Programming: Lecture 8 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University 9th February 2006 Jeff Linderoth IE417:Lecture 8 lehigh-logo Todays Outline Trust Regions Dogleg Example Convergence Proofs Homework for Next Time Jeff Linderoth IE417:Lecture 8 lehigh-logo Stuff We Learned Last Time Trust Regions, use model function, m k ( d ) : m k ( d ) def = f ( x k ) + d T f ( x k ) + 1 / 2 d T B k d Trust Region Subproblem (TRS) d k arg min d k { m k ( d ) } Control of Trust Region depends on parameter k : k def = f ( x k )- f ( x k + d k ) m k (0)- m k ( d k ) = Predicted Reduction Actual Reduction Jeff Linderoth IE417:Lecture 8 lehigh-logo Trust Region Algorithm 1 Solve TRS to get d k 2 Evaluate k 3 Adjust TR If k < 1 / 4 , Shrink: k +1 = 1 / 4 d k Else If k > 3 / 4 and d k = k , Grow: k +1 = 2 k Else k +1 = k 4 Move? [0 , 1 / 4) If k > , Step: x k +1 = x k + d k Else Stay: x k +1 = x k 5 Go to 1....
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This note was uploaded on 02/29/2008 for the course IE 417 taught by Professor Linderoth during the Spring '08 term at Lehigh University .

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lecture8 - lehigh-logo IE417: Nonlinear Programming:...

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