Using Sedumi in Yalmip

[Paul]

New to yalmip and I am using the following code to test how yalmip works to solve sdp problem:

P = sdpvar(3,3);

cons = [P >= 0,P(2,2)==1];

options = sdpsettings('Solver','Sedumi');

obj = [P(1,1)+P(1,3)];

solvesdp(cons,obj,options);

PP = double(P)

PP(1,1)+PP(2,3)

and the results are 

PP =

    1.2900    0.0000   -2.2900

    0.0000    0.0000    0.0000

   -2.2900    0.0000    5.8700

ans =

    1.2900

I am just too curious about the results, in the constraints, I have P(2,2)==1, however, in the results, PP(2,2)=5.87, which is not 1, why does this happen?? Anyone can help?

[Mark L. Stone]

The problem as written is unbounded, i.e., the optimal objective value is minus infinity.  You would benefit from using 'verbose',2 in sdpsettings.  And actually, not that it "helps", but your PP(2,2) is 0.000000000362895, which is not 1, but neither is it 5.87 (which is your PP(3,3)).

[Johan Löfberg]

Exactly.

You should always look at the diagnostic information supplied by the solver, and the information returned by solvesdp

solvesdp(cons,obj,options)
SeDuMi 1.3 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
...
Primal infeasible, dual improving direction found.
iter seconds  |Ax|    [Ay]_+     |x|       |y|
  5      0.5   0.0e+00   4.5e-15   0.0e+00   6.4e+00

ans =

    yalmiptime: 1.240000000000006e-01
    solvertime: 4.369999999999994e-01
          info: 'Unbounded objective function (SeDuMi-1.3)'
       problem: 2

This is to be expected. You can let P(1,3) go to -infinity and compensate that by letting P(3,3) go to infinity even faster

[Paul]

Thanks very much for the answer. YALMIP is really awesome, it is quite convenient to use. Thank you for developing this.

Best regards.