How to use fmincon on an symbolic integral function

Update: just rewrote my question... should be clear now...

I was trying to use fmincon to find the optimizer x=[x(1),x(2)] of a integral function where x(1) and x(2) are in the expression of the lower and higher limits of the integral, but I failed a lot of attempts which has driven me crazy!!!! Could someone help? A simple example to illustrate my problem, I want to find values for x and y to minimize function: integral(z^2,x,y)=(y^3)/3-(x^3)/3, such that 0<=x<=1,2<=y<=5.

Below are the code I wrote:

fun=@(x,y) int(@(z) z^2,x,y);

a0=[0,0];

sol=fmincon(fun,a0,[],[],[],[],[0,2],[1,5]);

Of course the code does not work and feedbacks are:

Error using symengine>makeFhandle/@(x,y)x.^3.*(-1.0./3.0)+y.^3.*(1.0./3.0) Not enough input arguments.
Error in fmincon (line 564)
      initVals.f = feval(funfcn{3},X,varargin{:});
Error in test (line 12)
sol=fmincon(ht,a0,[-1,-1],0)
Caused by:
    Failure in initial user-supplied objective function evaluation.
    FMINCON cannot continue.

Answer 1

[Mischa Kim]

Sylvia, use integral2 in combination with fmincon.

[Sylvia1008]

Thank you, but can you show me how? I don't see how that's the key problem I'm facing...

Answer 2

[Walter Roberson]

fun = @(xy) integral(@(z) z^2, xy(1), xy(2));
a0 = [0,0];
sol = fmincon(fun,a0,[-1,-1],0);

[Sylvia1008]

Does not really work...

Answer 3

[Alan Weiss]

I do not understand your example, but perhaps a completely new start will help you. Suppose that you have a parameterized function of x and y, say with parameter a:

 f = sin(a*x.^3)./3 - cos(a*y.^3)./3

Suppose that you want to minimize the integral of this function over 0 <= x <= 1, 1 <= y <= 2, and for -5 <= a <= 1.

 fun = @(a)integral2(@(x,y)sin(a*x.^3)./3 - cos(a*y.^3)./3,0,1,1,2);
 [asolution,intval] = fminbnd(fun,-5,1)

 asolution =
   -3.3592

 intval =
   -0.1405

You see, I defined the objective function of a as an integral, and found the minimum value of the integral over values of a in the interval -5 <= a <= 1.

Alan Weiss

MATLAB mathematical toolbox documentation