How can I show that the Least Square solution x = (A'.A)^-1.A'.y
Is different when A is an orthogonal matrix compared to an
overdetermined or underdetermind matrix.

Preferably transform the matrix using Singular Value Decomposition (SVD)
or something similar.

Thanx

I am playing around with Linear least squares. I have this system of equations

problem := ur+dr, {con1, con4, con5}, seq(w[i] = 0 .. 1, i = 1 .. N):
problem_matrix_form := Optimization:-Convert:-AlgebraicForm:-LPToMatrix(problem):

Optimization:-LPSolve(problem, maximize = true);
Optimization:-LPSolve(problem_matrix_form[2 .. 4], maximize = true);


The above trick-conversion method works for all LP and QP problems
However it does not work on NLP problems. I have attached the workshet

Why do I get this error message:


X := proc (a, b) local w, V, i, E, s; global Nr, sampvar, u;

w := sampvar*(1-a-b);     V[2] := u[1]^2;

if w = 0 then w := 0.1e-4 end if;

for i from 3 to Nr-1 do V[i] := w+a*u[i-1]^2+b*V[i-1] end do;

for i from 2 to Nr-1 do E[i] := -(1/2)*ln(V[i]^2)-u[i]^2/V[i] end do;

s[1] := 0;   for i from 2 to Nr-1 do s[i] := s[i-1]+E[i] end do;

s[Nr-1]

end proc:

So, I am reading the blog post about Mean Absolute Deviation portfolio optimization that

http://yetanothermathprogrammingconsultant.blogspot.com/2010/04/portfolio-from-qp-to-lp.html

claims that the traditional portfolio optimization problem can be expressed as seen below:

I am not sure however that it is 100% correct for example you have (r[i,t...