Lecture18

Lecture18 - Advanced Mathematical Programming IE417 Lecture...

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Advanced Mathematical Programming IE417 Lecture 18 Dr. Ted Ralphs
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IE417 Lecture 18 1 Reading for This Lecture Sections 8.8-8.9
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IE417 Lecture 18 2 Methods for Large Problems Conjugate gradient methods are based on the same idea of deflecting the gradient to get conjugate directions. However, they use a much simpler scheme. These methods are generally not as robust and are less efficient than quasi-Newton methods. However, they are much more practical for large problems. Quasi-Newton methods are generally impractical for more than 100 variables.
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IE417 Lecture 18 3 Conjugate Gradient Methods Idea : Let the next search direction depend on the last one, i.e. d j +1 = -∇ f ( y j +1 ) + α j d j As before, we require that directions produced be H-conjugate when f is quadratic. There are various choices for α j , depending on the assumptions one makes. However, all choices coincide for quadratic functions when performing exact line search.
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IE417 Lecture 18 4 Fletcher-Reeves Method
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Lecture18 - Advanced Mathematical Programming IE417 Lecture...

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