Minimizing a cost with constraint - lsqnonlin

Hi, I'm pretty new to minimisation/optimisation algorithm and am very confused as to why my code doesn't work properly. Basically I am confused about lsqnonlin and fsolve I would like to enforce the equation xprimhat'*F*xhat = 0 while lsqnonlin is running but am unsure as to how to do this.

Also I'm not sure if my euclidean distance is right since the doc stated that lsqnonlin squares and sums the cost itself? I'm not sure how that influences my code.

Could anyone please tell me how I could enforce this constraint?

Thanks a lot or your help.

function [Fmin, Pprim] = minimizeFundM( F, P, Pprim, X, Xprim, cloudP, e2_skew)
  options = optimset('Algorithm','levenberg-marquardt', 'Display', 'off');
  Pprim = lsqnonlin(@(in)distance(X, Xprim, F, cloudP, P, in), Pprim, [],[], options);
  Ppseud = pinv(P);
  Fmin = e2_skew*Pprim*Ppseud;
end

function d = distance(x, xprim, F, cloudP, P, Pprim) 
  % backproject points
  xhat = P*cloudP;
  xprimhat = Pprim*cloudP;

    %epipolar constraint
    constraint = @(xhat) xprimhat'*F*xhat;
    options = optimset('Algorithm','levenberg-marquardt', 'Display', 'off');
    xhat = fsolve(constraint, xhat, options);

    %euclidean distance
    dist = x - xhat;
    dist2 = xprim - xprimhat;

    d = sqrt(sum(dist.^2+dist2.^2)); 
  end

Answer 1

[Matt J]

You should be using fmincon, rather than lsqnonlin, if you have a nonlinear objective and constraints more complicated than simple upper and lower bounds. Beyond that, we cannot tell you if your function is "right", because only you know what optimization problem you are trying to solve! However, it appears that you have attempted to stick constraint enforcement inside your distance() objective function in some way, which I suspect is not what you truly want to do.