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Subject: Quadratic Cost Function x^T Q x
Date: Thu, 20 May 2010 15:50:21 +0000 (UTC)
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Hello,

I have a (quadratic) non-linear problem of the type x^T Q x.

Specifically the non-convex objective function is given by

J = SUM ||x^T Qi x||^2

for i <= 3.

My goal is to find arg min x, i.e. the values for the vector x.

Q is a symmetric 3 x 3 matrix and x is a vector of length 3. This is why i <= 3 since we have 3 parameters (unknowns) in x.

I am currently using lsqnonlin to find a solution. However I am getting trapped in local minima if I don't use a good starting guess for vector x. 

My question is, can I use something more 'robust' than lsqnonlin?
Furthermore is there actually a global minimum in my problem? 

What would be the best way to find it?

Many thanks.