Optimization via an Integral

Hey there, I would like to maximize a function W=5*si0-int(r0,0,si0*n0), where si0 and n0 are the decision variables and r0=(n0*si0)^2. Constraints are just nonnegativity of si0 and n0. Script copied from the editor:

function W=kiratest;
syms si0
syms n0
r0=(n0*si0).^2
W=-(5.*si0-int(r0,0,si0*n0));

I already tried fmincon and linprog, but I always get several errors, such as:

>> fmincon(@kiratest,[0 0],[-1 0;0 -1],[0;0])
Warning: Trust-region-reflective algorithm does not solve this type of problem,
using active-set algorithm. You could also try the interior-point or sqp
algorithms: set the Algorithm option to 'interior-point' or 'sqp' and rerun. For
more help, see Choosing the Algorithm in the documentation. 
> In fmincon at 472
??? Error using ==> kiratest
Too many input arguments.

Error in ==> fmincon at 590
      initVals.f = feval(funfcn{3},X,varargin{:});

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

AND:

>> linprog(@kiratest,[-1 0;0 -1],[0;0])
??? Error using ==> linprog at 132
LINPROG only accepts inputs of data type double.

Please help me find the mistake or else another solution for optimization. Sincerely, Kira

Answer 1

[Matt J]

The fmincon error is because you've defined no input arguments for kiratest(). If si0, n0 are the decision variables, then the vector [si0,n0] should be its input. Because of the missing input arguments, it's hard to know what your objective function is really meant to be, but I'm guessing it is

 function W=kiratest(x);

   si0=x(1);
   n0=x(2);

   W=-(5.*si0 - (si0*n0)^3/3);  %did the integral by hand

 end

Also, you should use fmincon's "lb" argument to express the positivity constraints

   fmincon(@kiratest,[0 0],[],[],[],[],[0;0],[]).

As for LINPROG, the error is due to you passing it a function handle argument @kiratest, which is not the kind of input it accepts. In any case, your problem does not appeat to be a linear program, so linprog will not be applicable.

[Kira]

Hey Matt, yes thank you, you are right about the input and lb of course. However, I guess the core problem is the integral (since I am able to make fmincon work without it). So now:

function W=kiratest(v); si0=v(1); n0=v(2); r0=(n0*si0).^2; W=-(5.*si0-int(r0,0,n0*si0));

GETS ME:

??? Undefined function or method 'int' for input arguments of type 'double'.

Error in ==> kiratest at 5 W=-(5.*si0-int(r0,0,n0*si0)); Error in ==> fmincon at 590 initVals.f = feval(funfcn{3},X,varargin{:});

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

So I would really appreciate further help. Best regards, Kira

[Matt J]

Please highlight your code and format it using the

toolbar button, so that it is more readable.