Minimize the Sum of Square error using optimization

I want to minimize the SSE using optimization: Suppose the expression is

where Q_r is the given set of data, u_r, v_r \in [0,1], and

If we choose m=n=3, then the P_i,j (control point) in 2nd expression of Main equation shoud be 16. So, it mean we have 16 unkown control points. How we can setup an objective function and optimization setup that the E (SSE) is minimum by finiding best P_i,j.

Answer 1

[Matt J]

I think you can do the whole optimization analytically. In particular, rewrite E as,

where A and B are r*m and n*r matrices poopulated using Ψ. Then the analytical solution is given by,

K=kron(B.',A);

P=reshape(  K(1:r+1:end,:)\Q   ,r,r);