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(solution) 2 Consider the optimization problem min { x 1 þ x 2 juð p Þ x 2 S x 2 1 where u : R k


2 Consider the optimization problem min { x 1 þ x 2 juð p Þ x 2 S x 2 1 where u : R k ! x 1 R is a smooth function, with u(0) = 1/2. Show that when p = 0, the point x = y (0) = [-1 1h] T is the unique minimizer for this problem. Prove that there exists a smooth function y : U ! R 2 defined over an appropriately small neighborhood U of the origin 0 in R k such that 8 p 2 U ; y ð p Þ is the unique minimizer for the problem with that value of p . Compute the derivative of the function y at p = 0.

 


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Sep 13, 2020

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