lecture5

# lecture5 - Today's Outline IE417 Nonlinear Programming...

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IE417: Nonlinear Programming: Lecture 5 Jeﬀ Linderoth Department of Industrial and Systems Engineering Lehigh University 31st January 2006 Jeﬀ Linderoth IE417:Lecture 5 Today’s Outline Review Exercises and. .. Rates of Convergence Jeﬀ Linderoth IE417:Lecture 5 Stuﬀ We Learned Last Time Line searches come in diﬀerent ﬂavors Exact/Inexact. Requiring derivatives/not requiring derivatives The kind most employed in practice is an inexact line search that requires gradients of f To know what step lengths are acceptable, we need conditions for suﬃcient decrease and suﬃcient curvature. Jeﬀ Linderoth IE417:Lecture 5 Acceptable Step Lengths Wolfe Conditions We can take any α that satisﬁes the Wolfe Conditions , for 0 < c 1 < c 2 < 1 f ( x k + αd k ) f ( x k ) + c 1 α f ( x k ) T d k d T k f ( x k + αd k ) c 2 f ( x k ) T d k If f ( x + αd ) is viewed as a one dimensional function φ ( α ) , then these conditions are equivalant to φ ( α ) φ

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lecture5 - Today's Outline IE417 Nonlinear Programming...

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