Not enough input arguments Been over the code so much need fresh eyes

clear; close all; clc;

x1 = linspace(-15,0); % Ao
x2 = linspace(-15,0); % Am
[X1,X2] = meshgrid(x1,x2);

% Variables
rho = 2710; % Density kg/m^3
beta = 1/12;
E = 69 * 10^6; % Gpa
sigmayield = 110 * 10^6; % MPa
Amin = 0.0001; % m^2
l = 0.5; % m
theta = 55 * pi/180; % degrees to radians
P = 500 * 10^-3; % kN
M = rho*(l*(2*sqrt(2)*X1+X2));

contour(X1,X2,M,75)
xlabel('x1')
ylabel('x2')
hold on

x0 = [0,0];
options = optimoptions(@fmincon,'Display','iter');
fun = @(x)Mass(rho,l,x);
[xstar,fstar] = fmincon(fun,x0,[],[],[],[],[],[],@Constraints,options)

Not enough input arguments.

Error in Prob5_13_Millett>Constraints (line 63)

c(1) = Amin-x(1);

Error in fmincon (line 650)

[ctmp,ceqtmp] = feval(confcn{3},X,varargin{:});

Caused by:

Failure in initial nonlinear constraint function evaluation. FMINCON cannot continue.

% Plot minimum point
plot(xstar(1),xstar(2),'r.','MarkerSize',20)
hold on

% Constraints
IneqCon1 = Amin-X1;
contourf(X1,X2,-IneqCon1,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold on
IneqCon2 = Amin-X2;
contourf(X1,X2,-IneqCon2,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold on
IneqCon3 = (1/sqrt(2))*((P*cos(theta))./X1)+((P*sin(theta))./(X2+sqrt(2).*X2))-sigmayield;
contourf(X1,X2,-IneqCon3,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold on
IneqCon4 = (sqrt(2)*P*sin(theta))/(X1+sqrt(2)*X2)-sigmayield;
contourf(X1,X2,-IneqCon4,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold on
IneqCon5 = (1/sqrt(2))*((P*sin(theta))/(X1+sqrt(2)*X2))-((P*cos(theta))/X1)-sigmayield;
contourf(X1,X2,-IneqCon5,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold on
IneqCon6 = -((1/sqrt(2))*((P*cos(theta))/X1)+((P*sin(theta))/(X1+sqrt(2)*X2)))-(pi^2*E*beta*X1)/(2*l^2);
contourf(X1,X2,-IneqCon6,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold on
IneqCon7 = -((sqrt(2)*P*sin(theta))/(X1+sqrt(2)*X2))-(pi^2*E*beta*X2)/(2*l^2);
contourf(X1,X2,-IneqCon7,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold on
IneqCon8 = -((1/sqrt(2))*((P*sin(theta))/(X1+sqrt(2)*X2))-((P*cos(theta))/X1))-(pi^2*E*beta*X1)/(2*l^2);
contourf(X1,X2,-IneqCon8,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
hold off

% Functions
function M = Mass(rho,l,x)
M = rho*(l*(2*sqrt(2)*x(1)+x(2)));
end
function [c,ceq] = Constraints(x,P,theta,Amin,sigmayield,E,beta)
c = zeros(8,1);
c(1) = Amin-x(1);
c(2) = Amin-x(2);
c(3) = (1/sqrt(2))*((P*cos(theta))/x(1))+((P*sin(theta))/(x(1)+sqrt(2)*x(2)))-sigmayield;
c(4) = (sqrt(2)*P*sin(theta))/(x(1)+sqrt(2)*x(2))-sigmayield;
c(5) = (1/sqrt(2))*((P*sin(theta))/(x(1)+sqrt(2)*x(2)))-((P*cos(theta))/x(1))-sigmayield;
c(6) = -((1/sqrt(2))*((P*cos(theta))/x(1))+((P*sin(theta))/(x(1)+sqrt(2)*x(2))))-(pi^2*E*beta*x(1))/(2*l^2);
c(7) = -((sqrt(2)*P*sin(theta))/(x(1)+sqrt(2)*x(2)))-(pi^2*E*beta*x(2))/(2*l^2);
c(8) = -((1/sqrt(2))*((P*sin(theta))/(x(1)+sqrt(2)*x(2)))-((P*cos(theta))/x(1)))-(pi^2*E*beta*x(1))/(2*l^2);
ceq = [];
end

Answer 1

[Steven Lord]

How does fmincon call the nonlinear constraint function? Specifically, how many inputs does it pass into that function? From that documentation page:

"nonlcon is a function that accepts a vector or array x and returns two arrays, c(x) and ceq(x)."

How many inputs are in the signature of your nonlinear constraint function?

"function [c,ceq] = Constraints(x,P,theta,Amin,sigmayield,E,beta)"

You're going to need to treat your constraint function like you did the objective function to pass the additional parameters into it.

[Walter Roberson]

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html

Answer 2

[Sam Chak]

Hi @Taylor Millett

The code for the fmincon part is now fixed and it returns a local minimum solution.

% Constants
rho         = 2710; % Density kg/m^3
beta        = 1/12;
E           = 69 * 10^6; % Gpa
sigmayield  = 110 * 10^6; % MPa
Amin        = 0.0001; % m^2
l           = 0.5; % m
theta       = 55 * pi/180; % degrees to radians
P           = 500 * 10^-3; % kN

% % contour plot
% x1      = linspace(-15,0); % Ao
% x2      = linspace(-15,0); % Am
% [X1,X2] = meshgrid(x1,x2);
% M       = rho*(l*(2*sqrt(2)*X1+X2));
% contour(X1,X2,M,75)
% xlabel('x1')
% ylabel('x2')
% hold on

% Calling fmincon to save me!
x0            = [1,1];
options       = optimoptions(@fmincon,'Display','iter');
fun           = @(x)Mass(rho,l,x);
[xstar,fstar] = fmincon(fun,x0,[],[],[],[],[],[],@Constraints,options)

                                            First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
    0       3    5.187519e+03    0.000e+00    9.581e+02
    1       6    5.186710e+03    0.000e+00    9.581e+02    2.067e-04
    2       9    5.029949e+03    0.000e+00    5.672e+02    4.013e-02
    3      12    7.074181e+02    0.000e+00    2.697e+00    1.167e+00
    4      15    4.193843e+00    0.000e+00    4.291e+00    2.090e-01
    5      19    6.251653e-01    0.000e+00    2.071e+02    1.076e-03
    6      27    7.925200e-01    0.000e+00    1.600e-04    9.099e-05

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

xstar = 1×2

1.0e-03 * 0.1149 0.2600

fstar = 0.7925

% %% Plot minimum point
% plot(xstar(1),xstar(2),'r.','MarkerSize',20)
% hold on
% 
% %% Constraints
% IneqCon1 = Amin-X1;
% contourf(X1,X2,-IneqCon1,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold on
% IneqCon2 = Amin-X2;
% contourf(X1,X2,-IneqCon2,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold on
% IneqCon3 = (1/sqrt(2))*((P*cos(theta))./X1)+((P*sin(theta))./(X2+sqrt(2).*X2))-sigmayield;
% contourf(X1,X2,-IneqCon3,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold on
% IneqCon4 = (sqrt(2)*P*sin(theta))./(X1+sqrt(2)*X2)-sigmayield;
% contourf(X1,X2,-IneqCon4,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold on
% IneqCon5 = (1/sqrt(2))*((P*sin(theta))./(X1+sqrt(2)*X2))-((P*cos(theta))./X1)-sigmayield;
% contourf(X1,X2,-IneqCon5,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold on
% IneqCon6 = -((1/sqrt(2))*((P*cos(theta))/X1)+((P*sin(theta))/(X1+sqrt(2)*X2)))-(pi^2*E*beta*X1)/(2*l^2);
% contourf(X1,X2,-IneqCon6,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold on
% IneqCon7 = -((sqrt(2)*P*sin(theta))/(X1+sqrt(2)*X2))-(pi^2*E*beta*X2)/(2*l^2);
% contourf(X1,X2,-IneqCon7,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold on
% IneqCon8 = -((1/sqrt(2))*((P*sin(theta))/(X1+sqrt(2)*X2))-((P*cos(theta))/X1))-(pi^2*E*beta*X1)/(2*l^2);
% contourf(X1,X2,-IneqCon8,[0 0],'r-','LineWidth',1.5','FaceAlpha',0.25)
% hold off

%% Functions
% Cost function
function M = Mass(rho,l,x)
    M = rho*(l*(2*sqrt(2)*x(1)+x(2)));
end

% Constraint function
function [c,ceq] = Constraints(x)
    % Constants
    rho         = 2710; % Density kg/m^3
    beta        = 1/12;
    E           = 69 * 10^6; % Gpa
    sigmayield  = 110 * 10^6; % MPa
    Amin        = 0.0001; % m^2
    l           = 0.5; % m
    theta       = 55 * pi/180; % degrees to radians
    P           = 500 * 10^-3; % kN
    
    % Constraints
    c    = zeros(8,1);
    c(1) = Amin-x(1);
    c(2) = Amin-x(2);
    c(3) = (1/sqrt(2))*((P*cos(theta))/x(1))+((P*sin(theta))/(x(1)+sqrt(2)*x(2)))-sigmayield;
    c(4) = (sqrt(2)*P*sin(theta))/(x(1)+sqrt(2)*x(2))-sigmayield;
    c(5) = (1/sqrt(2))*((P*sin(theta))/(x(1)+sqrt(2)*x(2)))-((P*cos(theta))/x(1))-sigmayield;
    c(6) = -((1/sqrt(2))*((P*cos(theta))/x(1))+((P*sin(theta))/(x(1)+sqrt(2)*x(2))))-(pi^2*E*beta*x(1))/(2*l^2);
    c(7) = -((sqrt(2)*P*sin(theta))/(x(1)+sqrt(2)*x(2)))-(pi^2*E*beta*x(2))/(2*l^2);
    c(8) = -((1/sqrt(2))*((P*sin(theta))/(x(1)+sqrt(2)*x(2)))-((P*cos(theta))/x(1)))-(pi^2*E*beta*x(1))/(2*l^2);
    ceq = [];
end