fmincon is giving error

Hi everyone, I have a very simple problem to solve 3 linear and one non linear equation using fmincon. I am using fmincon as I need to constrain my solution between lower and upper bound.

I write a function file as,myfun.m

______________________________________________________________________

function F=myfun(x,H2O,alpha,O2,K)

F=[x(2)+x(3)+x(4)-1;

    2*x(1)+4*x(4)-H2O-2*alpha;

    x(2)+2*x(3)-O2-alpha;

    K*x(4)-x(1)^2*(x(1)+x(2)+x(3)+x(4));

    ];
________________________________________________________________________

and the main file as, model.m, ______________________________________________________________________

H2O=0.8137;

O2=0.0785;

alpha=0.1;

K=1000;

x0=[.1,.1,.1,.1];

f = @(x)myfun(x,H2O,alpha,O2,K);

[x,fval]=fmincon(f,x0,[],[],[],[],[0;0;0;0],[1;1;1;1])

______________________________________________________________________

but fmincon is continuously giving error,as

Error using fmincon (line 618)

User supplied objective function must return a scalar value.

Error in model (line 10)

[x,fval]=fmincon(f,x0,[],[],[],[],[0;0;0;0],[1;1;1;1]);

I am using Matlab R2014b version.

Any help with be highly appreciable.

Thanks

Answer 1

[Torsten]

Define your linear and nonlinear equations as constraints for fmincon, not as parts of the objective function.

For the objective function, simply use f=@(x)0

Best wishes

Torsten.

Answer 2

[pietro]

fmincon must be used for monoobjective optimization so it expect a scalar value instead in your code he gets four different values. you should use any multiobjective optimization solver or converting to a monobjective problem by summing all elements of vectore F, like the following:

    function F=myfun(x,H2O,alpha,O2,K)

    F=[x(2)+x(3)+x(4)-1;

        2*x(1)+4*x(4)-H2O-2*alpha;

        x(2)+2*x(3)-O2-alpha;

        K*x(4)-x(1)^2*(x(1)+x(2)+x(3)+x(4));

        ];
     F=sum(F);
     end

[rabbahs]

Thanks Pietro for the reply. Please look at my reply below

Answer 3

[rabbahs]

Thanks Pieito and Torson for the reply, and I really appreciate you both to guide me.

so what I did

1) make an objfun.m file to define a funtion

function f=objfun(x,K)

f=(x(1)^2*(x(1)+x(2)+x(3)+x(4)))-(K*x(4));

2) make an main.m file to write the script,

L=5000;

xx=0.8173;

yy=0.0785;

alpha=0.1;

f=@(x)objfun(x,L);

x0=[.1 0.2 0.3 0.4];

Aeq=[0 1 1 1

    2 0 0 4

    0 1 2 0

    ];

beq=[1

    xx+2*alpha

    yy+alpha

    ];

lb=[0 0 0 0];

options = optimoptions('fmincon');

options = optimoptions(options,'Display', 'iter');

options = optimoptions(options,'Algorithm', 'active-set');

[x,fval,exitflag]=fmincon(f,x0,[],[],Aeq,beq,lb,[],[],options)

but it is still unable to find the feasible solution and give return the following msg,

No feasible solution found.

fmincon stopped because the size of the current search direction is less than twice the default value of the step size tolerance but constraints are not satisfied to within the default value of the constraint tolerance.

Answer 4

[Torsten]

As general solution for your above linear system I get

x1 arbitrary

x2=x1+1.31285

x3=-0.5*x1-0.567175

x4=-0.5*x1+0.254325

As you can see: whatever positive number you choose for x1 - the variable x3 will always be negative. So your problem has no feasible solution.

By the way:

If you modify your problem, choose the objective function to be zero - it will make things easier for the solver.

Best wishes

Torsten.

[rabbahs]

Hi Torsten,

Should I put (x(1)^2(x(1)+x(2)+x(3)+x(4)))-(K*x(4)) as a nonlinear constraint ? and put f=0 in objfun.m ? it that what you mean ?

best wishes

[Torsten]

No.

I mean that for the linear constraints you defined above, there is no feasible solution with nonnegative components. Adding the nonlinear constraint won't heal this.

You will have to go back to the roots and check your problem definition again.

Best wishes

Torsten.