# Looking for optimization libraries to optimize a matrix

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!

• You can't get smaller than the trivial A=0 and b=0. Maybe there is another condition that you want to be fullfilled? – chtz May 13 '17 at 16:44

## 1 Answer

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`

• I does not matter that the equation depends quadratically on x_i, since they are known. – chtz May 13 '17 at 16:46