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I have to find x that minimizes:

sigma{k}(x'*A_k*x - b_k)^2

where A_k are 4 x 4 positive definite matrices (A_1, A_2,...A_k), x is 4 x 1 vector and b_k are scalars (b_1,b_2,...b_k). Is there a function to solve this OP in MATLAB such that x will always be a global minimum? I would highly appreciate suggestions.

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