How can I find an optimised set of vectors

Question

Jonah Berean-Dutcher 2020-11-25

回答： Chaitanya Mallela 2020-12-22

I have a set of orthonormal vectors,

. There are b-many of them. I want to form other vectors, v, using these as basis vectors, i.e.

here the

are the coefficients in these linear combinations. Essentially, I want to find a new set of b-many vectors,

, which are all mutually orthonormal, and hence form a basis for the same space. However, I want these vectors

to be optimised, in that they minimize some function,

i.e. I'd be minimising C. Is there a form of constrained optimisation, implementable in MATLAB, that would allow me to do this?

Answer 1

Chaitanya Mallela 2020-12-22

Refer the documentation for the Constrained Optimization Algorithms