lecture7 - Today’s Outline IE417: Nonlinear Programming:...

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Unformatted text preview: Today’s Outline IE417: Nonlinear Programming: Lecture 7 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University Review Trust Regions 7th February 2006 lehigh-logo lehigh-logo Jeff Linderoth IE417:Lecture 7 Jeff Linderoth IE417:Lecture 7 Stuff We Learned Last Time Fun With Regular Expressions 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 2 3 What problems can you solve? for i in $MASTSIF/*.SIF; do grep -l ".*[QSO]UR2-.*-0$" $i; done If x0 is “sufficiently close” to x∗ , then {xk } → x∗ {xk } converges Q-quadratically to x∗ { f (xk ) } → 0 at a Q-quadratic rate. There are 157 problems in all! lehigh-logo lehigh-logo Jeff Linderoth IE417:Lecture 7 Jeff Linderoth IE417:Lecture 7 The Worst Linesearch Ever! Beale function [alphastar, fevals, gevals] = linesearch(x0,d) % linesearch performs a simple linesearch of the function % in ufn (enabled via cute) in the direction d % Input: x0 = base point % d = direction % Output: alphastar: step length % evals: number of function evaluations fevals = 0; gevals = 0; alphastar = 1; f (x) = (−3/2 + x1 (1 − x2 )2 ) + (−2.25 + x1 (1 − x2 )2 )2 + (−2.625 + x1 (1 − x2 )3 )2 lehigh-logo lehigh-logo Jeff Linderoth IE417:Lecture 7 Jeff Linderoth IE417:Lecture 7 In Our Next Episode... Great CUTEr Site http://www.sor.princeton.edu/∼rvdb/ampl/nlmodels/ cute/ Homework: (For next Tuesday): Turn in 4.1 Try 4.6, 4.9, 4.10 Write your linesearch. I’ll put scripts for running on the web. lehigh-logo Jeff Linderoth IE417:Lecture 7 ...
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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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lecture7 - Today’s Outline IE417: Nonlinear Programming:...

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