Nonlinear equality constraint is not met in MultiStart, but is met only using fmincon in loops?

I tried to use fmincon and wrote a loop for multiple starts. There was an inequality nonlinear constraint which restrict the vector norm to be one. I also tried to use Multistart with fmincon. Both are calling the same objective and constraint function files. However, the solutions from the former one met the vector norm = 1 constraint, but the Multistart solution didn't.

Here is my code for the Multistart with fmincon. tau is the parameter I am trying to solve.

obj = @(tau)ObjFunKDE(tau, beta1Est, Xs, n, nkde);
con =@(tau) ConstFminconKDE(tau, gamma0Est, gamma1Est, Xs, n, nkde, kappa);
tau0 = [-1/sqrt(3) 1/sqrt(3) 1/sqrt(3) ]';
opts = optimset('Algorithm','interior-point');
problem = createOptimProblem('fmincon','objective', obj,'x0',tau0,  'nonlcon',con, 'options',opts);
ms = MultiStart('StartPointsToRun', 'all', 'Display','iter');
[tau,fval] = run(ms,problem,50);

The nonlinear constraint function ConstFminconKDE is

function [c, ceq] = ConstFminconKDE(tau, gamma0Est, gamma1Est, Xs, n, nkde, kappa)
    w = Xs * tau;
    v = Xs * gamma1Est;
    wv =[w, v];

      hSqr = [ n^(-2/6)*var(w) , n^(-2/6)*var(v) ];
      rng(2,'twister');
      wvRs = datasample(wv, nkde, 'replace', true) + mvnrnd( [0 0], hSqr, nkde);    
      wRs = wvRs(:, 1);
      vRs = wvRs(:, 2);

      meanSign = mean(sign(wRs) .* vRs);
      c = meanSign +  mean(Xs * gamma0Est) - kappa;
     ceq = tau(1)^2 + tau(2)^2 + tau(3)^2 - 1;
  end

Any insight would be appreciated!

[Alan Weiss]

I am not sure what is going on, but do you have any bounds on your tau variable? If so, perhaps you should incorporate those bounds in your problem, and ensure that MultiStart runs only those start points that are within the bounds, by setting the StartPointsToRun property to 'bounds'.

Alan Weiss

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