Index exceeds the number of array elements (1). Caused by: Failure in initial nonlinear constraint function evaluation. FMINCON cannot continue.

My OBJECTIVE FUNCTION:

function f=objective2(h,x,F_r,T_r,UA_r,n)
options.Display='off';
%FlowStreams
x(1)=F_r(1);
x(2)=h;
x(6)=x(1)-x(2);
x(3)=x(2);
x(7)=x(6);
x(4)=x(3);
x(8)=x(7);
x(5)=x(4);
x(9)=x(8);
x(10)=x(5)+x(9);
x(11)=F_r(11);
x(12)=x(11);
x(16)=F_r(16);
x(17)=x(16);
x(18)=F_r(18);
x(19)=x(18);
x(20)=F_r(20);
x(21)=x(20);
x(13)=F_r(13);
x(14)=x(13);
x(15)=x(14);


%TempDependent
x(n+1)=T_r(1);
x(n+2)=T_r(2);
x(n+6)=T_r(6);
x(n+11)=T_r(11);
x(n+13)=T_r(13);
x(n+16)=T_r(16);
x(n+18)=T_r(18);
x(n+20)=T_r(20);


%Temp Independent
d1=fsolve(@(k)solve1(k,x,UA_r,n),[T_r(7),T_r(17)],options);
x(n+7)=d1(1);
x(n+17)=d1(2);

d2=fsolve(@(k)solve2(k,x,UA_r,n),[T_r(8),T_r(19)],options);
x(n+8)=d2(1);
x(n+19)=d2(2);

d3=fsolve(@(k)solve3(k,x,UA_r,n),[T_r(9),T_r(21)],options);
x(n+9)=d3(1);
x(n+21)=d3(2);

d4=fsolve(@(k)solve4(k,x,UA_r,n),[T_r(3),T_r(15),T_r(14),T_r(12),T_r(4),T_r(5)],options);
x(n+3)=d4(1);
x(n+15)=d4(2);
x(n+14)=d4(3);
x(n+12)=d4(4);
x(n+4)=d4(5);
x(n+5)=d4(6);


q = roots([0.000505*(x(5) + x(9)) 0.444*(x(5) + x(9)) -(0.444*(x(5)*x(n+5) + x(9)*x(n+9)) + 0.000505*(x(5)*x(n+5)^2 + x(9)*x(n+9)^2))]);
    for k = 1:2
        if q(k) > x(n+5) && q(k) < x(n+9)
            x(n+10) = q(k);
            break;
        elseif q(k) > x(n+9) && q(k) < x(n+5)
            x(n+10) = q(k);
            break;
        elseif k == 2
            k=k+1;
        end
    end

    
    f=-x(n+10);

end

Please Help

Answer 1

[Walter Roberson]

constraint2 will be called with a vector the same size as the vector passed to the objective function. Your x0 in your fmincon call is the scalar value 130, so the vector being passed to the objective function and to the constraint function will be a scalar.

You are confusing yourself by talking about x0 and x but also using @(h) defining your objective function. The x that is built inside your objective2 is not the x that will be passed to your constraint function. Perhaps you might need to build that x vector inside your constraint function as well.

[BrokenDreams]

My interntions are

1)Predict the scalar value h.

2)The vector 'x' which is built up inside the objective function will be dependent on the value of h. I would like to maximise x(n+10). According to the constraints.

Pls suggest me how should i make the function call and necessary changes. Thanks for your time

[Walter Roberson]

Unfortunately, I cannot copy and paste from pictures of code.

Generally speaking: change your anonymous function call to constraints2 to match your anonymous function call to objective2 (passing in the same extra variables.) Then in constraints2, calculate all of the x values that you will need for your constraints. You should consider writing a small function that calculates the x values given h and the other needed variables and call it from objective2 and constraints2 both.

You are probably thinking that considering that you "already" calculated x in objective2 that you should be able to pass the calculated value to constraints2 instead of recalculating it. The difficulty with this is that any number of calls to objective2 can happen between calls to constraints2, and that any number of calls to constraints2 can happen in a row with different h values. fmincon goes through an initial gradient estimation during which it can ignore the non-linear constraints, and once it gets going, it might end up trying a number of different h values trying to find one that satisfies constraints before passing it the objective function.

[BrokenDreams]

I am sorry I have taken lot of your time. I have proceeded the same way you have mentioned. I am still getting an error message stating "Undefined variable h". I wrote the code with following things in mind:

1)Predict only h. Calculate the remaining x using the predicted h. That x has to follow the constraints written in the constraint2 function. x0 is the initial guess of h.

I am a noob.Thanks so much for your time.

CALLING FMINCON

x0=[130];
[y,fval]=fmincon(@(h)objective2(h,F_r,T_r,UA_r,n),x0,a,b,aeq,beq,lb,ub,@(x)constraint2(h,x,F_r,T_r,UA_r,n),options);

OBJECTIVE2 FUNCTION:

function f=objective2(h,F_r,T_r,UA_r,n)
x=myfun(h,F_r,T_r,n,UA_r);
f=-x(n+10);
end

CONSTRAINT2 FUNCTION:

function [c,ceq]=constraint2(h,x,F_r,T_r,UA_r,n)
ceq=[];

x=myfun(h,F_r,T_r,n,UA_r);

c(1)= x(n+6)-x(n+7);
c(2)= x(n+17)-x(n+16);
c(3)=10-x(n+16)+x(n+7);
c(4)=10-x(n+17)+x(n+6);
c(5)=x(n+7)-x(n+8);
c(6)=x(n+19)-x(n+18);
c(7)=10-x(n+18)+x(n+8);
c(8)=10-x(n+19)+x(n+7);
c(9)=x(n+8)-x(n+9);
c(10)=x(n+21)-x(n+20);
c(11)=10-x(n+20)+x(n+9);
c(12)=10-x(n+21)+x(n+8);
c(13)=x(n+2)-x(n+3);
c(14)=x(n+15)-x(n+14);
c(15)=10-x(n+14)+x(n+3);
c(16)=10-x(n+15)+x(n+2);
end

MYFUN FUNCTION:

function x =myfun(h,F_r,T_r,n,UA_r)
options.Display='off';
%FlowStreams
x(1)=F_r(1);
x(2)=h;
x(6)=x(1)-x(2);
x(3)=x(2);
x(7)=x(6);
x(4)=x(3);
x(8)=x(7);
x(5)=x(4);
x(9)=x(8);
x(10)=x(5)+x(9);
x(11)=F_r(11);
x(12)=x(11);
x(16)=F_r(16);
x(17)=x(16);
x(18)=F_r(18);
x(19)=x(18);
x(20)=F_r(20);
x(21)=x(20);
x(13)=F_r(13);
x(14)=x(13);
x(15)=x(14);


%TempDependent
x(n+1)=T_r(1);
x(n+2)=T_r(2);
x(n+6)=T_r(6);
x(n+11)=T_r(11);
x(n+13)=T_r(13);
x(n+16)=T_r(16);
x(n+18)=T_r(18);
x(n+20)=T_r(20);


%Temp Independent
d1=fsolve(@(k)solve1(k,x,UA_r,n),[T_r(7),T_r(17)],options);
x(n+7)=d1(1);
x(n+17)=d1(2);

d2=fsolve(@(k)solve2(k,x,UA_r,n),[T_r(8),T_r(19)],options);
x(n+8)=d2(1);
x(n+19)=d2(2);

d3=fsolve(@(k)solve3(k,x,UA_r,n),[T_r(9),T_r(21)],options);
x(n+9)=d3(1);
x(n+21)=d3(2);

d4=fsolve(@(k)solve4(k,x,UA_r,n),[T_r(3),T_r(15),T_r(14),T_r(12),T_r(4),T_r(5)],options);
x(n+3)=d4(1);
x(n+15)=d4(2);
x(n+14)=d4(3);
x(n+12)=d4(4);
x(n+4)=d4(5);
x(n+5)=d4(6);


q = roots([0.000505*(x(5) + x(9)) 0.444*(x(5) + x(9)) -(0.444*(x(5)*x(n+5) + x(9)*x(n+9)) + 0.000505*(x(5)*x(n+5)^2 + x(9)*x(n+9)^2))]);
    for k = 1:2
        if q(k) > x(n+5) && q(k) < x(n+9)
            x(n+10) = q(k);
            break;
        elseif q(k) > x(n+9) && q(k) < x(n+5)
            x(n+10) = q(k);
            break;
        elseif k == 2
            k=k+1;
        end
    end



end

[Walter Roberson]

[y,fval]=fmincon(@(h)objective2(h,F_r,T_r,UA_r,n),x0,a,b,aeq,beq,lb,ub,@(h)constraint2(h,x,F_r,T_r,UA_r,n),options);