MATLAB: Fmincon check gradients fail

check gradientfinitedifferencestepsizefminconoptimization

I'm trying to provide vectorized gradients for my constraints of my 'nonlincon' function to reduce the run time.
My optimization problem has 11 variables from x1 to x11 and my 'nonlincon' calculates 6 constraints so my gradient matrix is 11 by 6
i tried to mimic how fmincon calculates delta for finite differences.
but when i use check gradients with gradient constraint options the check gradients fails no matter what value i use for finite difference step size.
is there something wrong with how i am calculating the gradients or my delta?
this is the options i used with fmincon
  options_fmincon = optimoptions('fmincon','ConstraintTolerance', 0.001,'Diagnostics','on','Display','iter-detailed','PlotFcn',{@optimplotx,@optimplotfunccount,@optimplotfval,@optimplotconstrviolation,@optimplotstepsize,@optimplotfirstorderopt},'OptimalityTolerance',0.001,'SpecifyConstraintGradient',true,'CheckGradients',true,'FiniteDifferenceStepSize',0.01,'TypicalX',ones(1,11));
The code is like this :
% fmincon Nonlinear constraints function
function [C, CEQ, Jacobian, DCEQ] = NonLinCon(X, LUT, IN_SPEC)
 DOF.M(1).A = X(1);
 DOF.M(2).A = X(2);
 DOF.M(3).A = X(3);
 DOF.M(4).A = X(4);
 DOF.M(5).A = X(5);
 DOF.M(1).B = X(6);
 DOF.M(2).B = X(7);
 DOF.M(3).B = X(8);
 DOF.M(4).B = X(9);
 DOF.M(5).B = X(10);
 DOF.IB = X(11)*1e-3;
DOF.C = IN_SPEC.C;          
DOF.D = IN_SPEC.D;
DOF.E = IN_SPEC.E;
DOF.F = IN_SPEC.F;
DOF.G = IN_SPEC.G;
DOF.H = IN_SPEC.H;
DOF.M(6).A = DOF.M(5).A;
DOF.M(6).B = DOF.M(5).B;
[~, OUT_SPEC] = calculatespecs(LUT,DOF);
if nargout > 2
    T_X = ones(1,11);
   v = ones(1,11);
   delta = v.*sign(X).*max(abs(X),T_X);
        Xp = X;
        DOF_p = DOF;
 DOF_p.M(1).A = [Xp(1) + delta(1), Xp(1), Xp(1), Xp(1), Xp(1), Xp(1), Xp(1), Xp(1), Xp(1), Xp(1), Xp(1)];
 DOF_p.M(2).A = [Xp(2), Xp(2) + delta(2), Xp(2), Xp(2), Xp(2), Xp(2), Xp(2), Xp(2), Xp(2), Xp(2), Xp(2)];
 DOF_p.M(3).A = [Xp(3), Xp(3), Xp(3) + delta(3), Xp(3), Xp(3), Xp(3), Xp(3), Xp(3), Xp(3), Xp(3), Xp(3)];
 DOF_p.M(4).A = [Xp(4), Xp(4), Xp(4), Xp(4) + delta(4), Xp(4), Xp(4), Xp(4), Xp(4), Xp(4), Xp(4), Xp(4)];
 DOF_p.M(5).A = [Xp(5), Xp(5), Xp(5), Xp(5), Xp(5) + delta(5), Xp(5), Xp(5), Xp(5), Xp(5), Xp(5), Xp(5)];
 DOF_p.M(1).B = [Xp(6), Xp(6), Xp(6), Xp(6), Xp(6), Xp(6) + delta(6), Xp(6), Xp(6), Xp(6), Xp(6), Xp(6)];
 DOF_p.M(2).B = [Xp(7), Xp(7), Xp(7), Xp(7), Xp(7), Xp(7), Xp(7) + delta(7), Xp(7), Xp(7), Xp(7), Xp(7)];
 DOF_p.M(3).B = [Xp(8), Xp(8), Xp(8), Xp(8), Xp(8), Xp(8), Xp(8), Xp(8) + delta(8), Xp(8), Xp(8), Xp(8)];
 DOF_p.M(4).B = [Xp(9), Xp(9), Xp(9), Xp(9), Xp(9), Xp(9), Xp(9), Xp(9), Xp(9) + delta(9), Xp(9), Xp(9)];
 DOF_p.M(5).B = [Xp(10), Xp(10), Xp(10), Xp(10), Xp(10), Xp(10), Xp(10), Xp(10), Xp(10), Xp(10) + delta(10), Xp(10)];
 DOF_p.IB = [Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3, Xp(11)*1e-3 + delta(11)];
 
 DOF_p.M(6).A = DOF_p.M(5).A;
 DOF_p.M(6).B = DOF_p.M(5).B;
        
        [~, OUT_SPEC_p] = calculatespecs(LUT,DOF_p);
       
        Jacobian(:,1) = abs((double(OUT_SPEC_p.A) - double(OUT_SPEC.A)) ./ delta);
        Jacobian(:,2) = abs((double(OUT_SPEC_p.B) - double(OUT_SPEC.B)) ./ delta);
        Jacobian(:,3) = abs((log10(double(OUT_SPEC_p.C)) - log10(double(OUT_SPEC.C))) ./ delta);
        Jacobian(:,4) = abs((double(OUT_SPEC_p.D) - double(OUT_SPEC.D)) ./ delta);
        Jacobian(:,5) = abs((double(OUT_SPEC_p.E) - double(OUT_SPEC.E)) ./ delta);
        Jacobian(:,6) = abs((double(OUT_SPEC_p.F) - double(OUT_SPEC.F)) ./ delta);
    DCEQ = [];
end
C(1) = IN_SPEC.A ./ double(OUT_SPEC.A) - 1;
C(2) = IN_SPEC.B ./ double(OUT_SPEC.B) - 1;
C(3) = log10(IN_SPEC.C) ./ log10(double(OUT_SPEC.C)) - 1;
C(4) = IN_SPEC.D ./ double(OUT_SPEC.D) - 1;
C(5) = IN_SPEC.E ./ double(OUT_SPEC.E) - 1;
C(6) = IN_SPEC.F ./ double(OUT_SPEC.F) - 1;
CEQ = [];
    
end

Best Answer

CheckGradient uses central differences, whereas you appear to be using right handed differences. Are you certain that your constraints are differentiable?
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