lecture2 - Today’s Outline IE417 Nonlinear Programming...

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Unformatted text preview: Today’s Outline IE417: Nonlinear Programming: Lecture 2 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University Say Cheese! Take 2 Some Quick Definitions Taylor’s Theorem Optimality Conditions for Unconstrained Optimization Methods for Unconstrained Optimization Line Search Trust Region 19th January 2006 Steepest Descent and Newton’s Method Jeff Linderoth IE417:Lecture 2 Jeff Linderoth IE417:Lecture 2 Last Time For Our Reference Taylor’s Theorem If f : Rn → R is (twice) continuously differentiable, then 1 2 3 Canonical Problem (and Transformations) Function Convexity/Concavity Set Convexity f (x + p) = f (x) + pT f (x + tp) for some t ∈ (0, 1). Also 1 f (x + p) = f (x) + pT f (x) + pT 2 for some t ∈ (0, 1) 2 f (x + tp)p Jeff Linderoth IE417:Lecture 2 Jeff Linderoth IE417:Lecture 2 In Our Next Episode... Homework to Turn In: 2.1. Also plot contours of f (x), and plot f (1, 2)T Suggested Problems to Try: 2.1–2.15, Save for 2.10 and 2.11 Maybe a little more lecture on Chapter 2 – but mostly problems! Jeff Linderoth IE417:Lecture 2 ...
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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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lecture2 - Today’s Outline IE417 Nonlinear Programming...

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