[Csdp] Help to use CSDP in SDP program

[Wendel Melo]

Thanks so much, Brian! You have written a matlab code to my problem!!! I
have no words! I have already been studying your example! Thanks one more
time!

Have a nice end of year

Wendel Melo

2012/12/26 Brian Borchers <borchers.brian at gmail.com>

>
>
>
> On Tue, Dec 25, 2012 at 9:17 PM, Wendel Melo <wendelalexandre at gmail.com>wrote:
>
>> Hi experts
>>
>>
>> I have a simple SDP problem to solve. Let Q be a constant symmetric
>> matrix and R the decision variable. My model is:
>>
>> min tr(R)
>> subject to:
>>
>> Q + R is positive semidefinite
>> R is positive semidefinte
>>
>>
>> But, reading the CSDP manual, i saw the CSDP form is:
>>
>> min tr(CR)
>> subject to:
>>
>> A(X) = a
>> X is positive semidefinite
>>
>
> That should be "tr(CX)" subject to "A(X)=a."  Note that in the MATLAB
> interface to CSDP (which is built for compatibility with SeDuMi), we solve
> problems with the minimization objective.
>
> This is different in the C interface to CSDP, where we solve problems of
> the form:
>
> max tr(CX)
> A(X)=b
> X is positive semidefinite.
>
> Switching between max and min is trivial (just change the sign of C) and
> the MATLAB interface does the work for you.
>
>
>>
>>
>> Is there a way of writting my model in the CSDP form?
>>
>
>>
> Yes there is.  The idea is to make the X matrix a block diagonal matrix of
> the form:
>
> X=[X11 0; 0 X22]
>
> where
>
> X11=R
> X22=R+Q
>
> Then the problem becomes
>
> min tr(CX)
> X22-X11=Q
> X is positive semidefinite
>
> where
>
> C=[I 0; 0 0]
>
> This requires linear equality n*(n+1)/2 constraints (one for each element
> in the upper triangle of R+Q.)
>
> I've attached a MATLAB code and sample output showing how this can be done
> using the MATLAB interface to CSDP.
>
>


-- 
Wendel
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