To find the dual of the L2 norm we have to solve the problem max ux x 2 1 , which requires to find a vector x on the unit circle, with maximal projection on u Clearly, the optimal solution x must be a unit norm vector, parallel to u Hence, u uT u u 2 u 2 Thus, we conclude that the Euclidean norm L2...

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To find the dual of the L2 norm we have to solve the problem max{ux ||x||2 1},

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To find the dual of the L2 norm we have to solve the problem

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An Introduction To Financial Markets A Quantitative Approach

ISBN: 9781118014776

1st Edition

Authors: Paolo Brandimarte

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Question Posted: Apr 03, 2024 03:00 AM

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To find the dual of the L2 norm we have to solve the problem max{ux ||x||2 1},

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max{ux ||x||2 1}, which requires to find a vector x on the unit circle, with maximal projection on u. Clearly, the optimal solution x* must be a unit norm vector, parallel to u. Hence, u uT |u|| = ||u||2. ||u||2 Thus, we conclude that the Euclidean norm L2 is self-dual.

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An Introduction To Financial Markets A Quantitative Approach

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