Unique solution of a non-convex OP

Question

I have to find $x$ that minimizes: $$\|x^H\textbf Ax - b\|_2^2 = \sum_{k}(x^H\textbf A_kx - b_k)^2$$ where $A_k$ are 4 x 4 positive definite matrix($A_1, A_2,...A_k$), $x$ is 4 x 1 vector and $b_k$ are scalars ($b_1,b_2,...b_k)$. I have solved this OP by using MATLAB functions but each time $x$ is different even though its a very close estimate. Is there any method to solve this OP in a way that it always gives the same $x$?

Answer 1

As per this, a non-convex problem has multiple locally optimal points and hence, finding a global optimum might be a tedious task.