why Fmincon code result are infeasible

Hello,

I dont know why the code for fmincon does not attention to linear constraint A, b and the results that gives me is obviously infeasible.

In A the first element asks t1 has to be larger than 1 but the result gives me t1=0.3

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% Wheelchair
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function Wheelchair

%     clc;
    clear all; close all;
    
    dp=design_parameters; % Generate structure variable containing all design parameters
    
    f=@(x)objective_function(x,dp); % Objective function handle
    nonlcon=@(x)nonlinear_constraints(x,dp); % Nonlinear constraint function handle
    
    lb=[dp.X1_min;dp.X2_min;dp.X3_min;dp.X4_min];% Design variable bounds
    ub=[dp.X1_max;dp.X2_max;dp.X3_max;dp.X4_max]; % Design variable bounds
    
    x0=[16e-3;0.8e-3;12e-3;0.7e-3]; % Initial design point
    A=[0,-(0.68*dp.db*dp.sigmau)/(0.3*dp.mb*dp.g),0,0;-1/dp.X1_min,0,0,0;1/dp.X1_max,0,0,0;0,-1/dp.X2_min,0,0;0,1/dp.X2_max,0,0;0,0,-1/dp.X3_min,0;0,0,1/dp.X3_max,0;0,0,0,-1/dp.X4_min;0,0,0,1/dp.X4_max];
    b=[-1,-1,1,-1,1,-1,1,-1,1];
    
    % Minimization using fmincon and the specified options:
    options=optimoptions('fmincon','Display','iter','OptimalityTolerance',1e-12,'ConstraintTolerance',1e-6,'StepTolerance',1e-12);
    [x,fval]=fmincon(f,x0,A,b,[],[],lb,ub,nonlcon,options);
    
    % Display of the optimal design results:
    disp(['Optimal value of d1: ',num2str(1000*x(1)),' mm']);
    disp(['Optimal value of t1: ',num2str(1000*x(2)),' mm']);
    disp(['Optimal value of d2: ',num2str(1000*x(3)),' mm']);
    disp(['Optimal value of t2: ',num2str(1000*x(4)),'mm']);
     disp(['Optimal value of f: ',num2str(fval),' kg']);

end

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function dp=design_parameters

    dp.L1=0.82; %(m)
    dp.L2=0.691; %(m)
    dp.L3=0.270; %(m)
    dp.L4=0.04; %(m)
    dp.L5=1.59; %(m)
    dp.L6=0.627; %(m)
    dp.L7=0.568; 
    dp.Lad=0.601; 
    dp.Lss=0.4; 
    
    dp.mb=300; 
    dp.Rho=2700; 
    dp.g=10;
    
    dp.db=6e-3; 
    dp.sigmau=110e6; 
    dp.E=68e9;
    dp.K=2.1; 
    dp.deltamax=1e-3; 
 

    dp.X1_min=14e-3; dp.X1_max=20e-3; % Minimum/maximum length of rectangular (mm)
    dp.X2_min=0.e-3; dp.X2_max=0.7e-3; %
    dp.X3_min=10e-3; dp.X3_max=14e-3; % 
    dp.X4_min=0.5e-3; dp.X4_max=0.7e-3; 
    
end
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function f=objective_function(x,dp)
A1=(x(1)/2)^2-(x(1)/2-x(2))^2;
A2=(x(1)/2-x(2))^2-(x(1)/2-2*x(2))^2;
A3=((x(1)+2*x(2))^2-(x(1))^2)/4;
A4=(x(3)/2)^2-(x(3)/2-x(4))^2;


    f=2*((pi*A1*dp.L1*dp.Rho)+(pi*A1*dp.L2*dp.Rho)+(pi*A2*dp.L3*dp.Rho)+(6*pi*A3*dp.L4*dp.Rho)+(0.097))+((pi*A4*dp.L5*dp.Rho)+(pi*A4*dp.L6*dp.Rho)+(pi*A4*dp.L7*dp.Rho)); % 
    
end
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function [c,ceq]=nonlinear_constraints(x,dp)
A5=(x(1))^4-(x(1)-2*x(2))^4;

    
    c(10,1)=0.2*dp.mb*dp.g-((pi.^3* dp.E/(dp.K*dp.Lad)^2*64)*A5); % 
    c(11,1)=((dp.mb*dp.g/2)*(dp.Lss)^3/(48/64)*pi*A5)-dp.deltamax; % 
    
    
    ceq=[]; % There are no nonlinear equality constraints
    
end
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Answer 1

[Matt J]

There can't be any gaurantee that fmincon will be able to find a solution (for example, one may not exist), but fmincon is aware that a feasible solution was not found. This was made very clear in the exit message:

Converged to an infeasible point.

fmincon stopped because the size of the current step is less than

the value of the step size tolerance but constraints are not

satisfied to within the value of the constraint tolerance.

[Elmira Jafari]

Thanks matt. It is solved now.

for the project I have to select two algorithm as my obj is nonlinear and two nonlinear constraints I chose GA and Fmincon. but professor asked:

[Elmira Jafari]

[Elmira Jafari]

Two difierent methods must be selected in order to solve your optimization problem. The

choice of methods to use should be based on the nature of the problem. For each of the chosen

methods:

Provide a brief description

Describe the appropriateness of the method in solving your optimization problem

[Elmira Jafari]

Dear Matt

Can you give me a name of a refrence that cn provide me with these informations?