Optimization Questions on set constraint

Halo

I have got a question when setting the constraint of optimization I want to optimize the p(1,p(2)and p(3) There are 4 constraint i need to set

    1)p(1)+p(2)+p(3)=1
    2)p(1)*e(1)+p(2)*e(2)+p(3)*e(3)<=eav
    3)0<=p(i), where i=1,2,3
    4)p(i)<=1, where i=1,2,3

I want these set in a condition file However matlab just tell me

Warning: The default trust-region-reflective algorithm does not solve problems with the constraints you
have specified. FMINCON will use the active-set algorithm instead. For information on applicable
algorithms, see Choosing the Algorithm in the documentation. 
> In fmincon at 504
  In optst22 at 32 
Warning: Your current settings will run a different algorithm (interior-point) in a future release. 
> In fmincon at 509
  In optst22 at 32

PS it seems that it failure PLZ help me

Answer 1

[Matt J]

No, there is non evidence of failure. The messages are just warnings that fmincon switched to non-default settings.

Answer 2

[Ho Chun]

I have set the constraint that the range of p(1), p(2) and p(3) must within 0 and 1. However, they still have negative value appear. It seems that this constraint does not work.

May you tell me how to set constraint?

My code as follow

c(1)=p(1)*t*e(1)+p(2)*t*e(2)+p(3)*t*e(3);
c(2)=-p(1)*t;
c(3)=-p(2)*t;
c(4)=-p(3)*t;

c(5)=p(1)*t-1;
c(6)=p(2)*t-1;
c(7)=p(3)*t-1;

ceq=[-1+result;];

[Matt J]

Only bound constraints can be satisfied exactly, but only with the interior-point or sqp algorithm, and only if you use the lb,ub arguments to express them, as Alan indicated.

The rest of the constraints can be violated slightly and you must accept this. Although, you can use the TolCon input option to demand a lower non-zero violation. The price will be more iterations and longer compute time for fmincon, however.

[Torsten]

If t=1, result=p(1)+p(2)+p(3) and your call to fmincon is correct, I don't see anything wrong.

By the way: The constraints p(i)<=1 are superfluous because you claim p(i)>=0 and p(1)+p(2)+p(3)=1.

Best wishes

Torsten.

Answer 3

[Alan Weiss]

You should not be using nonlinear constraints. Instead, use bounds and linear constraints as follows:

 lb = zeros(3,1)
 ub = ones(3,1)
 Aeq = [1,1,1]; beq = 1;
 A = [e(1),e(2),e(3)]; b = eav;
 options = optimoptions(@fmincon,'Algorithm','interior-point');
 [x,fval,eflag,outpt] = fmincon(fun,x0,A,b,Aeq,beq,lb,ub,[],options)

For more information, see the documentation on constraints.

Alan Weiss

MATLAB mathematical toolbox documentation