matlab optimization

Hello everyone:
Here is an optimization problem,

maximize y

subject to:

x(2)*y-x(1)+2*x(2)<=0;
x(2)*y+x(1)-4*x(2)<=0;
x(3)*y-x(1)+1*x(3)<=0;
x(3)*y+x(1)-3*x(3)<=0;
0.222*x(3)*y-x(2)+0.333*x(3)<=0;
0.5*x(3)*y+x(2)-1*x(3)<=0;
x(1)+x(2)+x(3)=1;
x(1)>0;
x(2)>0;
x(3)>0;

The solution to the above problem when solved using GRG based solver
in excel is
y=0.838
x(1)=0.538
x(2)=0.170
x(3)=0.292

My question is how give initial points to above problem just guess
"y" when using optimization toolbox or is it necessary to mention
x(1), x(2) and x(3) in initial guess if so how to mention it

Thanx in advance

If I understand your question correctly, the answer
is yes, one needs to supply an initial guess to *all*
the unknowns - in your case to the x's and y.

One way to do this is to call "y" x(4):

maximize x(4) subject to
x(2)*x(4)-x(1)+2*x(2)<=0, etc

and thus your unknown is the vector
x = [x(1), ..., x(4)]. Please see the doc
for examples on how to pass the initial guess
(it's very easy).

-marcelo

Srihari wrote:
> Hello everyone:
> Here is an optimization problem,
>
> maximize y
>
> subject to:
>
> x(2)*y-x(1)+2*x(2)<=0;
> x(2)*y+x(1)-4*x(2)<=0;
> x(3)*y-x(1)+1*x(3)<=0;
> x(3)*y+x(1)-3*x(3)<=0;
> 0.222*x(3)*y-x(2)+0.333*x(3)<=0;
> 0.5*x(3)*y+x(2)-1*x(3)<=0;
> x(1)+x(2)+x(3)=1;
> x(1)>0;
> x(2)>0;
> x(3)>0;
>
> The solution to the above problem when solved using GRG based solver
> in excel is
> y=0.838
> x(1)=0.538
> x(2)=0.170
> x(3)=0.292
>
> My question is how give initial points to above problem just guess
> "y" when using optimization toolbox or is it necessary to mention
> x(1), x(2) and x(3) in initial guess if so how to mention it
>
> Thanx in advance