How can I find an optimised set of vectors

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]

Refer the documentation for the Constrained Optimization Algorithms

https://www.mathworks.com/help/optim/ug/constrained-nonlinear-optimization-algorithms.html