I am writing a code for using "fmincon" but it is having some error, Why?

I am writing the following code. I am not able to find the error? I am new to MATLAB.

dbstop if error
clear all
clc
format longEng
kv = 0.5; kh = 0.1;
r0 = 5; H = 5;
q = 20; a = 1;
b = 0; gamma = 18.4;
omega = 25; phi = 39*(pi/180);

lambda = kv/kh;
syms x(i)
% fun = @(x)A1 /((lambda*A1)+A2)
L = r0*(sin(x(2))*exp((x(2)-x(1))*tan(phi))-sin(x(1)))
% % % % Rate of work due to soil weight in static condition

f1 = -(1/3)*(1/(9*((tan(phi))^2)+1)*(exp(3*(x(2) - x(1))*tan(phi))*(3*tan(phi)*sin(x(2))-cos(x(2)))-(3*tan(phi)*sin(x(1))-cos(x(1)))))
f2 = -(1/6)*(L/r0)*cos(x(2))*exp(x(2)-x(1))*tan(phi)*(2*sin(x(1))+(L/r0))
f3 = -(1/3)*(H/r0)*(sin(x(1)))^2
W1 = (1-kv)*gamma*omega*((r0)^3)*(f1-f2-f3)
% Rate of work due to strip load
Wqs = -(1-kv)*omega*q*b*(a+(b/2)+r0*sin(x(1)))


% % % % Rate of work due to soil weight with kh

fq1 = -(1/3)*(1/(9*((tan(phi))^2)+1)*(exp(3*(x(2) - x(1))*tan(phi))*(3*tan(phi)*cos(x(2))+sin(x(2)))-(3*tan(phi)*cos(x(1))+sin(x(1)))))
fq2 = -(1/3)*(L/(r0)^2)*cos(x(2))*exp(x(2)-x(1))*tan(phi)*(cos(x(1))-(H/r0))
fq3 = -(1/6)*(H/r0)*sin(x(1))*(2*cos(x(1))-(H/r0))
W1kh = kh*gamma*omega*((r0)^3)*(fq1-fq2-fq3)
% Rate of work due to strip load
Wqskh = -kh*omega*q*b*r0*exp((x(2)-x(1))*tan(phi))*cos(x(2))


% Yield acceleration coefficients (ky)
A1 = gamma*omega*((r0)^3)*(f1-f2-f3) - omega*q*b*(a+(b/2)+r0*sin(x(1)))
A2 = omega*q*b*r0*exp((x(2)-x(1))*tan(phi))*cos(x(2)) - gamma*omega*((r0)^3)*(fq1-fq2-fq3)
fun = @(x)A1 /((lambda*A1)+A2)

lb = [0,0];
ub = [3.14,3.14];
A = [];
b = [];
Aeq = [];

beq = []; 
x0 = [0,0];  
nonlcon = [];
x = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)  

[Matt J]

What error messages (copy/pasted) is it giving you?

Answer 1

[Matt J]

Your objective function is not returning numbers. It is returning sym variables, e.g.,

>> fun([0,0])

ans =

(6.7465e+03*sin(x(1)) - 2.7771e+03*cos(x(1)) + 2.7771e+03*exp(2.4294*x(2) - 2.4294*x(1))*(cos(x(2)) - 2.4294*sin(x(2))) + 1.9167e+04*sin(x(1))^2 - 4.6563e+04*exp(x(2) - 1*x(1))*cos(x(2))*(sin(x(1)) + exp(0.8098*x(2) - 0.8098*x(1))*sin(x(2)))*(0.1667*sin(x(1)) - 0.1667*exp(0.8098*x(2) - 0.8098*x(1))*sin(x(2))))/(3.0955e+04*sin(x(1)) - 2.0632e+04*cos(x(1)) + 1.3885e+04*exp(2.4294*x(2) - 2.4294*x(1))*(cos(x(2)) - 2.4294*sin(x(2))) + 2.7771e+03*exp(2.4294*x(2) - 2.4294*x(1))*(2.4294*cos(x(2)) + sin(x(2))) + 9.5833e+04*sin(x(1))^2 - 9.5833e+03*sin(x(1))*(2*cos(x(1)) - 1) - 2.3281e+05*exp(x(2) - 1*x(1))*cos(x(2))*(sin(x(1)) + exp(0.8098*x(2) - 0.8098*x(1))*sin(x(2)))*(0.1667*sin(x(1)) - 0.1667*exp(0.8098*x(2) - 0.8098*x(1))*sin(x(2))) + 4.6563e+04*exp(x(2) - 1*x(1))*cos(x(2))*(cos(x(1)) - 1)*(0.0667*sin(x(1)) - 0.0667*exp(0.8098*x(2) - 0.8098*x(1))*sin(x(2))))

>> whos ans

Name Size Bytes Class Attributes

ans 1x1 8 sym

[Matt J]

lb = [0,0];
ub = [3.14,3.14];
A = [];
b = [];
Aeq = [];

beq = [];
x0 = [0,0];
nonlcon = [];
x = fmincon(@fun,x0,A,b,Aeq,beq,lb,ub,nonlcon)

Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current step is less than
the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

x = 1×2

2.2538 3.1342

function fval = fun(x)
    
    kv = 0.5; kh = 0.1;
    r0 = 5; H = 5;
    q = 20; a = 1;
    b = 0; gamma = 18.4;
    omega = 25; phi = 39*(pi/180);
    
    lambda = kv/kh;
    
    % fun = @(x)
    L = r0*(sin(x(2))*exp((x(2)-x(1))*tan(phi))-sin(x(1)));
    % % % % Rate of work due to soil weight in static condition
    
    f1 = -(1/3)*(1/(9*((tan(phi))^2)+1)*(exp(3*(x(2) - x(1))*tan(phi))*(3*tan(phi)*sin(x(2))-cos(x(2)))-(3*tan(phi)*sin(x(1))-cos(x(1)))));
    f2 = -(1/6)*(L/r0)*cos(x(2))*exp(x(2)-x(1))*tan(phi)*(2*sin(x(1))+(L/r0));
    f3 = -(1/3)*(H/r0)*(sin(x(1)))^2;
    W1 = (1-kv)*gamma*omega*((r0)^3)*(f1-f2-f3);
    % Rate of work due to strip load
    Wqs = -(1-kv)*omega*q*b*(a+(b/2)+r0*sin(x(1)));
    
    
    % % % % Rate of work due to soil weight with kh
    
    fq1 = -(1/3)*(1/(9*((tan(phi))^2)+1)*(exp(3*(x(2) - x(1))*tan(phi))*(3*tan(phi)*cos(x(2))+sin(x(2)))-(3*tan(phi)*cos(x(1))+sin(x(1)))));
    fq2 = -(1/3)*(L/(r0)^2)*cos(x(2))*exp(x(2)-x(1))*tan(phi)*(cos(x(1))-(H/r0));
    fq3 = -(1/6)*(H/r0)*sin(x(1))*(2*cos(x(1))-(H/r0));
    W1kh = kh*gamma*omega*((r0)^3)*(fq1-fq2-fq3);
    % Rate of work due to strip load
    Wqskh = -kh*omega*q*b*r0*exp((x(2)-x(1))*tan(phi))*cos(x(2));
    
    
    % Yield acceleration coefficients (ky)
    A1 = gamma*omega*((r0)^3)*(f1-f2-f3) - omega*q*b*(a+(b/2)+r0*sin(x(1)));
    A2 = omega*q*b*r0*exp((x(2)-x(1))*tan(phi))*cos(x(2)) - gamma*omega*((r0)^3)*(fq1-fq2-fq3);
    
    
    fval = A1 /((lambda*A1)+A2);
    
end

[Akshay Pratap Singh]

Thanks Matt J, It solved my problem.

Thank you very much.