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lecture7 - Today's Outline IE417 Nonlinear Programming...

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lehigh-logo IE417: Nonlinear Programming: Lecture 7 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University 7th February 2006 Jeff Linderoth IE417:Lecture 7 lehigh-logo Today’s Outline Review Trust Regions Jeff Linderoth IE417:Lecture 7 lehigh-logo Stuff We Learned Last Time A Horrible Proof of Kantorovich Inequality Rate of Convergence: Newton’s Method Assume we take Newton steps: If 2 f ( x ) exists and is Lipschitz continuous around the optimal solution x * (at which the second order sufficient conditions hold), then 1 If x 0 is “sufficiently close” to x * , then { x k } → x * 2 { x k } converges Q-quadratically to x * 3 { ∇ f ( x k ) } → 0 at a Q-quadratic rate. Jeff Linderoth IE417:Lecture 7 lehigh-logo Fun With Regular Expressions What problems can you solve? for i in \$MASTSIF/*.SIF; do grep -l ".*[QSO]UR2-.*-0\$" \$i; done There are 157 problems in all! Jeff Linderoth IE417:Lecture 7

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lecture7 - Today's Outline IE417 Nonlinear Programming...

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