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I need to solve the problem shown below, but I do not know what optimization libraries can solve this problem.
The optimization target is a 3x3 matrix A and a 3D vector b, given the 3D vectors xi where i=1,2,...,N.
I need a C/C++ optimization library, hopefully open source, light and fast. If you have any idea, help me. I would appreciate more if you let me know the related class or method in the library. Thank you!
In your place I would unpack the matrix to a vector. From this point, we have a continuous, vectoric, but nonlinear problem. It is nonlinear, because it depends quadratically from x. But it is very easily derivable, and surely doesn't have separate local optimum-points.
Thus it can be easily solved by any nonlinear optimization solution, I would suggest org.apache.commons.optim.nonlinear.
