In fmincon I set the linear constraint x1+x2+x3=12, but the sum of decision variables in the iteration result does not meet the condition

I saved the changes of three decision variables in the iteration process. At the end of the iteration, each variable tends to be stable, but does not meet the linear constraints I set.

Here is the variable change process, the sum of varaible is 11 not 12

[Torsten]

To give a useful comment, we have to see your code.

[Matt J]

In addition to what Torsten said, you should be checking the exitflag to see if fmincon even believes the optimization succeeded.

[汉森 戴]

hope you can give me some suggestion.

here is my code（four portfolio total）

1st： (main.m)

clc;clear;

%% Parameter initialization

bb = [0.3 0.4 0.3]; pp = [5 5 5]; mm = [4.5 5 6]; cc = [1 5 7];nn = 13.6; TKK = [6 1 2 3]; REE = [11 13 15];

namda = [4:1:13]; %namda is the sum of decision variables

xx = [];

for i=1:length(namda)

%The optimal solution module is substituted

[x, y(i)] = M2Mallocation(bb,pp,mm,cc,namda(i),TKK,REE);

xx = [xx,sum(x)]; %Verify that the decision variable sum satisfies the linear constraint (whether the sum of x is namda)

end

figure(1);

stem(xx);

figure(2);

plot(namda,y,':r*');hold on;

2nd: (optf.m)

function f = optf(x) %Objective function

global b c p m c

f = b(1).*(1/(m(1)-x(1)) + 1/(m(2)-x(2)) + 1/(m(3)-x(3)))...

+ b(2).*(x(1).*c(1)/(m(1)-x(1)) + x(2).*c(2)/(m(2)-x(2)) + x(3).*c(3)/(m(3)-x(3)))...

+ b(3).*(x(1).*p(1)/(m(1)-x(1)) + x(2).*p(2)/(m(2)-x(2)) + x(3).*p(3)/(m(3)-x(3)));

3rd: (limf.m)

function [g,h] = limf(x) %Nonlinear constraints

global p m TK RE

g = [1/(m(1) - x(1))-TK(1)+TK(2);1/(m(2) - x(2))-TK(1)+TK(3);1/(m(3) - x(3))-TK(1)+TK(4);...

x(1).*p(1)/(m(1) - x(1))-RE(1);x(2).*p(2)/(m(2) - x(2))-RE(2); x(3).*p(3)/(m(3) - x(3))-RE(3)];

h = [];

4th:(M2Mallocation.m)

function [x,y] = M2Mallocation(b1,p1,m1,c1,n1,TK1,RE1)

global b m c n TK RE p

b = b1; p = p1; m = m1; c = c1; n = n1; TK = TK1; RE = RE1;

options = optimoptions('fmincon',...

'Algorithm','sqp',...

'StepTolerance',1e-5, 'MaxFunctionEvaluations', 1e5,'OptimalityTolerance',1e-40,...

'ConstraintTolerance',1e2,'MaxIter', 10);

[x,y] = fmincon('optf',ones(3,1),[],[],[1,1,1],n,[],[m(1);m(2);m(3)],...

'limf', options);

i make a experiment on this code，namda is the sum of decision variables（Linear constraints in fmincon）,so i traverse namda then take the the sum of x in result to determine whether the x of the output is satisfied with linear constraints（x1 + x2 + x3 = namda）.the result is that at beginning the linear constraint is satisfied at first, but it is not satisfied later.

theoretically, the two points should be 12 and 13.

[汉森 戴]

but in picture(mode = 1),decision variables tend to stabilize and converge during the iteration process，no change more.

Answer 1

[Torsten]

Tighten your ConstraintTolerance, and you'll see that fmincon converges to an infeasible point for n=12 and n=13.

1st： (main.m)

clc;clear;
%% Parameter initialization

bb = [0.3 0.4 0.3]; pp = [5 5 5]; mm = [4.5 5 6]; cc = [1 5 7];nn = 13.6; TKK = [6 1 2 3]; REE = [11 13 15];


namda = [4:1:13]; %namda is the sum of decision variables
xx = [];

for i=1:length(namda)
    %The optimal solution module is substituted
    [x, y(i)] = M2Mallocation(bb,pp,mm,cc,namda(i),TKK,REE);
    xx = [xx,sum(x)]; %Verify that the decision variable sum satisfies the linear constraint (whether the sum of x is namda)
end

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.


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.


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.


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.


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.


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.


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.


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.


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.


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.

figure(1);
stem(xx);

figure(2);
plot(namda,y,':r*');hold on;

2nd: (optf.m)

function f = optf(x) %Objective function
global b c p m c
f = b(1).*(1/(m(1)-x(1)) + 1/(m(2)-x(2)) + 1/(m(3)-x(3)))...
    + b(2).*(x(1).*c(1)/(m(1)-x(1)) + x(2).*c(2)/(m(2)-x(2)) + x(3).*c(3)/(m(3)-x(3)))...
    + b(3).*(x(1).*p(1)/(m(1)-x(1)) + x(2).*p(2)/(m(2)-x(2)) + x(3).*p(3)/(m(3)-x(3)));
end

3rd: (limf.m)

function [g,h] = limf(x) %Nonlinear constraints
global p m  TK RE
   g = [1/(m(1) - x(1))-TK(1)+TK(2);1/(m(2) - x(2))-TK(1)+TK(3);1/(m(3) - x(3))-TK(1)+TK(4);...
        x(1).*p(1)/(m(1) - x(1))-RE(1);x(2).*p(2)/(m(2) - x(2))-RE(2); x(3).*p(3)/(m(3) - x(3))-RE(3)];
   h = [];
end

4th:(M2Mallocation.m)

function [x,y] = M2Mallocation(b1,p1,m1,c1,n1,TK1,RE1)
global b  m c n TK RE p
 b = b1; p = p1; m = m1; c = c1; n = n1; TK = TK1; RE = RE1;

options = optimoptions('fmincon',...
    'Algorithm','sqp',...
    'StepTolerance',1e-5, 'MaxFunctionEvaluations', 1e5,'OptimalityTolerance',1e-40,...
    'ConstraintTolerance',1e-3,'MaxIter', 10);
[x,y,exitflag,~] = fmincon(@optf,ones(3,1),[],[],[1,1,1],n,[],[m(1);m(2);m(3)],...
    @limf, options);
end

[汉森 戴]

Thank you for your patience.I seem to got it.Unreasonable initialization parameters lead to fmincon conversions to an acceptable point （constraint failed）for n=12 and n=13.Am i right?

[Torsten]

I don't know what the reason is that your sum constraint cannot be satisfied.

Maybe it contradicts your constraints defined in limf - I didn't check it in detail.

[汉森 戴]

Thanks again for your answer.Let me check it