fmincon objective function problem

I need to maximize the following objective function in Matlab:

    mean (a*I'*x1+b*(ones(1,24)-I)'*x1)-mean((a*(ones(1,24)-I)'*y1)+(b*I'*y1))

I made two .m file: 1) In the objfun.m file I defined the objective function as:

    function f = objfun(x)
    f = mean (a*I'*x1+b*(ones(1,24)-I)'*x1)-mean((a*(ones(1,24)-I)'*y1)+(b*I'*y1));

2) In the second (main) .m file I have my parameters and calculations for a, b and I and also below constraints and fmincon:

    lb = [0,0];
    ub = [10,10];
    x0 = [1,2];
    [x,fval] = fmincon(@objfun,x0,[],[],[],[],lb,ub)

When I run the program I get below error for fmincon:

''Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.'' Would you please advise how can I fix this problem? Is there anything wrong with my objective function, as it is a function of x1 and y1 but I have objfun(x) only? Or do I call the function wrongly? Any help is appreciated!

Answer 1

[Walter Roberson]

Guessing about what a, b, x1, y1 are for:

First make sure x1 and y1 are defined.

Then

    f = @(ab) mean (ab(1)*I'*x1+ab(2)*(ones(1,24)-I)'*x1)-mean((ab(1)*(ones(1,24)-I)'*y1)+(ab*2)*I'*y1));

    lb = [0,0];
    ub = [10,10];
    x0 = [1,2];
    [ab,fval] = fmincon(@objfun,x0,[],[],[],[],lb,ub)
    a = ab(1); b = ab(2);

[Sara]

Thanks for your reply Walter! a and b are vectors(1x24) and have constant values. x1 and y1 are the variables that should be optimized(vectors 1x24) and I know the lower and upper values for them only. I tried your code in my main file (not in objfun.m) but still I get the same error :(

Answer 2

[Alan Weiss]

You need to put ALL of your control variables in one vector or matrix x.

function f = objfun(x,a,b,I)
x1 = x(1:24);
y1 = x(25:end);
f = mean (a*I'*x1+b*(ones(1,24)-I)'*x1)-mean((a*(ones(1,24)-I)'*y1)+(b*I'*y1));

Call the function like this, after you put the a, b, and I arrays in your workspace:

fun = @(x)objfun(x,a,b,I);
[x,fval] = fmincon(fun,...)

Alan Weiss

MATLAB mathematical toolbox documentation

[Sara]

Thanks Alan for your reply. I tried your code. First there was an error that Function definitions are not permitted in this contex. So, I made a new script and inserted

function f = objfun(x,a,b,I)

there. Then I got an error about x1 = x(1:24); so, I changed x1 and y1 to

x1 = sym('x', [1 24]); y1 = sym('x', [25 49]);

At the end I got the error message:

Output argument "f" (and maybe others) not assigned during call to "objfun".

Error in @(x)objfun(x,a,b,I)

Error in fmincon (line 534)
      initVals.f = feval(funfcn{3},X,varargin{:});

Error in draft1 (line 39)
[x,fval] = fmincon(fun,x0,[],[],[],[],lb,ub)

Caused by:
    Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.

[Alan Weiss]

Oh, I didn't know that you were trying to optimize symbolic variables. Basically, you either need to formulate your problem without using symbolic variables, or you need to convert your symbolic expressions to floating-point using matlabFunction as shown in Using Symbolic Mathematics with Optimization Toolbox Solvers.

However, most likely you do not need to do anything symbolically at all. Remember, MATLAB computes numerically, and so you just need to understand that fmincon is going to present your objective function with a numerical x that is, say, a 48-element vector. Your objective function simply needs to accept that vector and compute the value of the objective function. No symbolic math needed.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Sara]

Thanks for your response Alan! Now it works! But I get non-zero values for the first 25 items of my x vector (x1) and for the rest of items (24:end) optimization gives 0. I guess I need to define more constraints or add ''if'' statements in my code.