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December 1st, 2010, 02:34 AM   #1
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least absolute error minimization with quadratic constraint

Hello everyone,

I have the following optimization problem:

Given a set of N points of length=2 (the i-th point is written n_i) , find the point v (of norm 2) such that:
maximize the sum_i^N |n_i^T v|
with respect to ||v||=2

where n_i^T is the transpose of n_i.

In other words, I am looking for the point v that minimizes the sum of least absolute errors. The constraint ||v||=2 is quadratic. Thus, this system could be called least absolute error minimization with a quadratic constraint.

Does anyone have a solution for that kind of problems?

Benoit
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