Thread Subject: regarding fminsearch in Matlab

Hi,
I need to put a simple constraint and use fminsearch.
min f(x) subject to sum(x)=<1 (or preferably -1<sum(x)<1)
where x is a vector.
I can use fmincon, but it does not work well for my problem at. Any feedback would be greatly appreciated
Thanks

econgrad <hammadq80@gmail.com> wrote in message
<5111638.1216356287372.JavaMail.jakarta@nitrogen.mathforum.org>...
> Hi,
> I need to put a simple constraint and use fminsearch.
> min f(x) subject to sum(x)=<1 (or preferably -1<sum(x)<1)
> where x is a vector.
> I can use fmincon, but it does not work well for my
problem at. Any feedback would be greatly appreciated
> Thanks

Change the variables: pick one of your variables and replace
by the sum. Alternatively you can also use the 'cumsum'
variable. In other word, work on new multi-variable "y" with
this linear transformation y=P*x

minimize g(y) := f(inv(P)*y)

P = [1 0 ... 0
     0 1 ....0
     ...
     0 0 0 1 0
     1 1 1 1 1] % last variable is replaces by the sum

Or

P = [1 0 ... 0
     1 1 ... 0
     ...
     1 1 ... 1 0
     1 1 1 1 1 1]

Now the sum constraint on x becomes bound constraint on last
variable on y.: -1<=y(n)<=1

Use any bound constraint minimization algorithm, such as
this one
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=8277

Bruno

econgrad <hammadq80@gmail.com> wrote in message
<5111638.1216356287372.JavaMail.jakarta@nitrogen.mathforum.org>...
> Hi,
> I need to put a simple constraint and use fminsearch.
> min f(x) subject to sum(x)=<1 (or preferably -1<sum(x)<1)
> where x is a vector.
> I can use fmincon, but it does not work well for my problem at. Any
feedback would be greatly appreciated
> Thanks

(Why did fmincon fail to work well?)

Are there any other constraints on the problem?
If not, then you can easily enough transform this
into a bound constrained problem by a simple
transformation.

Suppose you have n variables, x1,...,xn.

Leave the first n-1 variables unchanged, but
your n'th variable will now become the sum of
all n unknowns. I'll call ir xsum. Compute the
actual value of xn inside your objective function
as

   xsum - x1 - x2 - x3

Now you can simply place a bound constraint
(both lower and upper bounds) on the sum of
the variables.

If you are unhappy with how fmincon worked,
then you can now use fminsearchbnd on this
simple bound constrained system. You can
even have bounds on the first n-1 unknowns.
The only problem is you will not be able to put
bounds on xn.

You can find fminsearchbnd on the file exchange.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?
objectId=8277&objectType=file

John

Thanks abunch Bruno

Thanks John,
I am not sure why fmincon failed. No, I dont have any other constraints. I think that fminsearch and fmincon are based on very different algorithms and fmincon seems to get stuck with some local/flat area much more easily. Based on my experience fminsearch works better.
Thanks for your input. It was very helpful