fmincon drives variables away from the solution

Hello,

I am trying to solve a constrained optimization problem for a vector function using fmincon. When I provide the initial point to my optimization problem equal to the true solution (I know what the true solution is), fmincon runs and then my output vector is totally away from the true solution.

Surprisingly, the value of the objective function evaluated at the true solution is 1.0027e-07 (theretically it should be ZERO). And the value of the objective function after running fmincon is 2.7724e-04. I am unsure why this is happening. I have posted my code snippets below. Thank you.

X0=[34.29; 0; 0.1490; 0.3341; 28.220; 0.2405];
%  TRUE PARAMS: b1 = 34.29; b2=0; b3=0.1490; b4=0.3341; P=28.220; E=0.2405;
y=matched_ests(:,2);
y_dot=matched_ests(:,3);
y_ddot=matched_ests(:,4);
y_tdot=matched_ests(:,5);
u=matched_ests(:,6);
opt_f = @(X)opt_func_sync_gen(X, y, y_dot, y_ddot, y_tdot, u);
options = optimoptions('fmincon', 'MaxIterations', 10000,...
          'MaxFunEvals', 10000, 'UseParallel', true);
A=[];
b=[];
Aeq=[];
beq=[];
lb = zeros(6,1);
ub=[100;100;100;100;100;100];
nonlcon = [];
[Y,fval] = fmincon(opt_f,X0,A,b,Aeq,beq,lb,ub,nonlcon,options);
b1 = Y(1);
b2 = Y(2);
b3 = Y(3);
b4 = Y(4);
P = Y(5);
E = Y(6);
fprintf('%.3f %.3f %.3f %.3f %.3f %.3f %.3f',b1,b2,b3,b4,P,E);

And the function used by fmincon is

function [obj_func_value] = opt_func_sync_gen(X, y, y_dot, y_ddot, y_tdot, u)

    b1 = X(1);
    b2 = X(2);
    b3 = X(3);
    b4 = X(4);
    P = X(5); 
    E = X(6); 

    sin_y = sin(y);
    cos_y = cos(y);
    vector_func = (E*b1*(sin_y).^2 - b4*P.*(sin_y) + b2*b4.*y_dot.*sin_y...
                + b4*y_ddot.*sin_y + b1*b3.*(sin_y.^2).*cos_y...
                + b2*(sin_y.*y_ddot - (y_dot.^2).*cos_y)...
                + P.*y_dot.*cos_y - b1.*sin_y.^2.*u ...
                + y_tdot.*sin_y - y_dot.*y_ddot.*cos_y).^2;

    obj_func_value = sum(vector_func);
end

Answer 1

[Alan Weiss]

Surprisingly, there was another question at nearly the same time that has a solution equivalent to yours. To quote my solution to that question:

By default, fmincon uses the 'interior-point' algorithm, which strictly stays away from bounds. If you want results exactly at the bounds, then I suggest that you use the 'sqp' algorithm. Set the algorithm using the Algorithm option.

Alan Weiss

MATLAB mathematical toolbox documentation

[shaunaksinha]

Hi Alan,

Using the 'sqp' algorithm solved the problem.

Thank you.