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From: atlasoglu on 17 Jul 2010 06:20
Hi people,
I couldn't find any help in help section of matlab, so I need you. I
have an objective function in matrix notation with constraints.
How can write a matlab formulation solve this maximization problem?


You can see the problem here: http://img257.imageshack.us/img257/289/problemu.png
From: Srikanth on 17 Jul 2010 10:53
On Jul 17, 3:20 am, atlasoglu <atlaso...(a)gmail.com> wrote:
> Hi people,
> I couldn't find any help in help section of matlab, so I need you. I
> have an objective function in matrix notation with constraints.
> How can write a matlab formulation solve this maximization problem?
>
> You can see the problem here:http://img257.imageshack.us/img257/289/problemu.png

The matrix constraints should be rewritten as vector/scalar
constraints. For example, for each column of the matrix Pi, you have:
Product of any two elements in a single column are zero
Sum of all the elements in a single column is one.
(The alternative approach could be to use mixed-integer programming.
Otherwise, this is a nonlinear problem).

A matrix equality constraint is an equality constraint on each of its
elements.

Since you are maximizing over Pi, Uo and R, be aware that this can be
a very big (dimensionally) problem.

hth
From: atlasoglu on 17 Jul 2010 15:20
On Jul 17, 5:53 pm, Srikanth <s...(a)xdtech.com> wrote:
> On Jul 17, 3:20 am, atlasoglu <atlaso...(a)gmail.com> wrote:
>
> > Hi people,
> > I couldn't find any help in help section of matlab, so I need you. I
> > have an objective function in matrix notation with constraints.
> > How can write a matlab formulation solve this maximization problem?
>
> > You can see the problem here:http://img257.imageshack.us/img257/289/problemu.png
>
> The matrix constraints should be rewritten as vector/scalar
> constraints. For example, for each column of the matrix Pi, you have:
> Product of any two elements in a single column are zero
> Sum of all the elements in a single column is one.
> (The alternative approach could be to use mixed-integer programming.
> Otherwise, this is a nonlinear problem).
>
> A matrix equality constraint is an equality constraint on each of its
> elements.
>
> Since you are maximizing over Pi, Uo and R, be aware that this can be
> a very big (dimensionally) problem.
>
> hth

Thanks Srikanth,

in fact I found a way about the problem of Pi. ( If you wonder, It is
introducing a Raw_Pi (1x(t*n) matrix) that takes only integer values
and each entry is nonnegative value that is not more than c. Doing
this way help us define a 1-1 onto correspondance from Raw_Pi set to
Pi set. )


After rewritting constraint as vectorel ones; what is next? How do I
tell to matLab "maximize the objective function given these and you
have to move in these constraint "

Your help really precious for me.



From: Alan Weiss on 19 Jul 2010 08:25
On 7/17/2010 3:20 PM, atlasoglu wrote:
> On Jul 17, 5:53 pm, Srikanth<s...(a)xdtech.com> wrote:
>> On Jul 17, 3:20 am, atlasoglu<atlaso...(a)gmail.com> wrote:
>>
>>> Hi people,
>>> I couldn't find any help in help section of matlab, so I need you. I
>>> have an objective function in matrix notation with constraints.
>>> How can write a matlab formulation solve this maximization problem?
>>
>>> You can see the problem here:http://img257.imageshack.us/img257/289/problemu.png
>>
>> The matrix constraints should be rewritten as vector/scalar
>> constraints. For example, for each column of the matrix Pi, you have:
>> Product of any two elements in a single column are zero
>> Sum of all the elements in a single column is one.
>> (The alternative approach could be to use mixed-integer programming.
>> Otherwise, this is a nonlinear problem).
>>
>> A matrix equality constraint is an equality constraint on each of its
>> elements.
>>
>> Since you are maximizing over Pi, Uo and R, be aware that this can be
>> a very big (dimensionally) problem.
>>
>> hth
>
> Thanks Srikanth,
>
> in fact I found a way about the problem of Pi. ( If you wonder, It is
> introducing a Raw_Pi (1x(t*n) matrix) that takes only integer values
> and each entry is nonnegative value that is not more than c. Doing
> this way help us define a 1-1 onto correspondance from Raw_Pi set to
> Pi set. )
>
>
> After rewritting constraint as vectorel ones; what is next? How do I
> tell to matLab "maximize the objective function given these and you
> have to move in these constraint "
>
> Your help really precious for me.
>
>
>
Minimize the negative of the objective function. See
http://www.mathworks.com/access/helpdesk/help/toolbox/optim/ug/brhkghv-3.html#brhkghv-5

Alan Weiss
MATLAB mathematical toolbox documentation
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