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Unformatted text preview: x for this NLP as described in KarushKuhnTucker Theorem. Using these conditions and the theorem, prove that x is optimal. b) Suppose that we replace the objective function by, min x 1 + x 2 . Indicate for what values of is x going to be optimal for (NLP). Exercise 3 (15 marks) . 1 2 a) Let g 1 , g 2 , g 3 : be defined by g 1 ( x ) := x, g 2 ( x ) := 2 , g 3 ( x ) := x. Plot these functions on 2 . Identify on your plot, the function g defined by, g ( x ) := max { g 1 ( x ) , g 2 ( x ) , g 3 ( x ) } . Prove that g is a convex function. b) Suppose g 1 , g 2 , . . . , g m : n are given convex functions. Define the function g : n where g ( x ) := max { g 1 ( x ) , g 2 ( x ) , . . . , g m ( x ) } . Prove that g is a convex function....
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This note was uploaded on 06/12/2011 for the course CO 250 taught by Professor Guenin during the Spring '10 term at Waterloo.
 Spring '10
 GUENIN

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