Lecture 9 - Class 9 February 3 This week Mon Wed Lecture...

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Class 9: February 3 This week: Mon, Wed: Lecture Friday: TA session For those who have not had an optimization course. See notes at end of these slides Read Wikipedia article referenced in those notes Read Appendix of textbook
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Constraints can be written in standard form for optimization with dual variables: Lagrangian: First Order Necessary Conditions: Stationary point: Complementary slackness: Stationary point, dual slackness interpretations? Characterizing Optimal Choice 0 Under y Unde x x r P ( ) Maximize u x ( ) 0 0 ( ) g x P x y h x x   scalar vector ( , , ) ( ) x u x g x h x   L ( , ) 0 0 0 0 ( ) 0 0 0 x x g x g x h x h x L
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First Order Necessary Conditions: Characterizing Optimal Choice ( , , ) ( ) x u x g x h x   L ( , , ) ( ) 0 x x u x g x h x     L       0 0 0 ( ) 0 0 0 g x g x h x h x ( ) u x g x h x ( ( ) ) g x P x x y h x   ( ( ) ) g x P h x I   1 0 0 1 I u x P I P 0 i i x for each i 0 P x y These are Karush Kuhn Tucker (KKT) conditions
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