lsqnonlin return a result optimized nothing

I am trying to implement a math algorithm as my final project for my CV class, which can be found here: paper

Simplify the problem is: Minimize

With constraint:

And I wrote a function for the lsqnonlin() to obtain the result:

if true
  function F = myfun(x, m, n, u, v, std_u, std_v)
% x = pm1 - pm13, x1,y1,z1,t1 - xn,yn,zn,tn
% m: # of picture
% n: # of point
% u: 2D points u direction i, j
% v: 2D points v direction i, j
F = 0;
for row = 1:m
  for column = 1:n
     Xi = x(1, 11+3*(n-1)+1);
     Yi = x(1, 11+3*(n-1)+2);
     Zi = x(1, 11+3*(n-1)+3);
     error1 = u(row, column)*( x(row, 9) * Xi + x(row, 10) * Yi + x(row, 11) * Zi + 1 ) - ( x(row, 1) * Xi + x(row, 2) * Yi + x(row, 3) * Zi + x(row, 4) );
     error2 = v(row, column)*( x(row, 9) * Xi + x(row, 10) * Yi + x(row, 11) * Zi + 1 ) - ( x(row, 5) * Xi + x(row, 6) * Yi + x(row, 7) * Zi + x(row, 8) );
     F = F +(error1)*(error1) / std_u*std_u + (error2) * (error2) / std_v * std_v;  
  end

    for column = 1:n
       Xi = x(1, 11+3*(n-1)+1);
       Yi = x(1, 11+3*(n-1)+2);
       Zi = x(1, 11+3*(n-1)+3);
       error3 = Xi * Xi + Yi * Yi + Zi * Zi;
       F = F + abs(error3);        
    end
end
end
  end

Where x is a matrix

X = [p1_11 - p1_33 , x1, y1, z1, t1, ...., xn, yn, zn, tn p2_11 - p2_33 , 0 ... 0 ... pm_11 - pm_33 , 0 ... 0] As i have to combine two parameter into one in order to use lsqnonlin(@F,X,[],[],options, 2, 40, u, v, val1, val2)

However, the function returned my initialed guess.

If you have any idea why this would happen please let me know

[Torsten]

As clearly written in the documentation of "lsqnonlin", the functions g_k must be returned separately, not their cumulated sum of absolute values.

So in your case, F must be a vector of size 2*(2*m*n+n), not a single scalar.

Furthermore, your quadratic constraint on the parameters to be fitted shows that "lsqnonlin" is not the correct tool to use, but "fmincon".

Best wishes

Torsten.

[junqi yang]

Thank you for the suggestion, I will give it a try.

[junqi yang]

Also, I used lsqnonlin because the author of that paper said they solve the equation by using levenberg-marquardt algorithm, and lsqnonlin is the only function can use levenberg-marquardt.