Hi there,

I am writing a program with quite a lot of constraints to solve a semidefinite feasibility problem but am having some troubles. Perhaps somebody here could help.

Within this program I have constraints such as

Y=sdpvar(27,27,'hermitian','complex')

constraint=set(Y>=0)
constraint=constraint+set(trace(A*Y)-trace(B*Y)==0)

where A and B are previously defined 27x27 hermitian matrices. I would just like to ask if constraints like the one above involving traces of multiplied matrices is valid?

My problem is that my code is telling me that all my feasibility problems are valid, when I know that some should not be. Any advice on this would be appreciated.

If so, please show the complete code and data, and point to the constraint which is infeasible in the solution that YALMIP/SeDuMi returns

In the problem you showed, Y=0 is a trivially feasible solution

Thanks - I have attached the matlab script I have been working on that should run if you just call it.

Lines 81 and 91, for example, should constrain some elements of the variable matrices to be non-zero. After that I have some constraints along the lines of what I wrote before.

I am in fact just trying to work through an academic paper to check that I have done things correctly (the actual problem can be found at arxiv.org/abs/quant-ph/0308032 on page 5 if it helps).

In order to test the program is working I have been using an example (on page 12 of that paper) for which the primal problem should be feasible if a<3 in the program and infeasible if a>3 - my problem is that a feasible solution is always found so either I have written some constraints that dont make sense or I made an error in the calculation.

Hopefully you could tell me whether the constraints make logical sense. If so, then at least I know I am just bad at quantum mechanics.

Regards

Ritat

And what do you mean when you say the solution is infeasible. Solve the problem and run



all numbers are zero, hence those constraints are feasible etc

BTW, note that your solutions Yi are all (numerically) real. Maybe you are adding a constraint f=0 when you really mean real(f)=0, or something like that

EDIT: NOw I read the last paragraph ofyour text. Well, the code looks correct, you must simply have made osme mistake somewhere-

Thank you very much - that has helped a lot. Before I wasn't sure if I was using YALMIP correctly but your reply is very useful. I will now start checking for calculation errors in my code.

Thanks!

Ritat