A 'Unbounded objective function (MOSEK)' problem happens while trying to solve a SOCP in Matlab

[wei chen]

Hi John, 

Thanks very much for creating this fantastic tool which makes things much easier. 

I'm currently using it in solving my SOCP problem in Matlab enviroment. The solver is MOSEK.

Now I have several questions in using it. Could you please have a look at them? I would highly appreciate your response.

And there is the code:

clear
clc
%%           <Variable statememt>
x = sdpvar (3, 1);
y = sdpvar (2, 1);
z = sdpvar (2, 1);
%%           <constraint statememt>
constraint = [ ];
constraint = [constraint, x(1,1)==12.66^2/sqrt(2)];
constraint = [constraint, x(2,1)>=0];
constraint = [constraint, x(3,1)>=0];
constraint = [constraint, y(1,1)>=0];
constraint = [constraint, y(2,1)>=0];
%------------------------------------The Rotated Quadratic Constraint---------
constraint = [ constraint, rcone( [y(1,1) ; z(1,1)], x(1,1), x(2,1) ) ];
constraint = [ constraint, rcone( [y(2,1) ; z(2,1)], x(2,1), x(3,1) ) ];
%%----------------------------------The Linear Constraint------------------
 constraint = [constraint, sqrt(2)*10.2195*x(2,1)-10.2195*(y(1,1)+y(2,1))+5.2088*(-z(1,1)+z(2,1)) == -0.10];
 constraint = [constraint, sqrt(2)*5.2088*x(2,1)-5.2088*(y(1,1)+y(2,1))-10.2195*(-z(1,1)+z(2,1)) == -0.06];
 constraint = [constraint, sqrt(2)*1.6106*x(3,1)-1.6106*y(2,1)+0.8203*(-z(2,1)) == -0.09];
 constraint = [constraint, sqrt(2)*0.8203*x(3,1)-0.8203*y(2,1)-1.6106*(-z(2,1)) == -0.04];        
%%----------------------------------Objective------------------
Objective =  y(1,1) +y(2,1) ;
%%----------------------------------Solve------------------------
constraint
ops = sdpsettings('solver','mosek','verbose',1,'debug',1);
sol = optimize(constraint,-Objective,ops);


if sol.problem == 0
 % Extract and display value
 solution_u = value(x)
 solution_R = value(y)
 solution_T = value(z)
else
 display('Hmm, something went wrong!');
 sol.info
 yalmiperror(sol.problem)
end

And there is the output of matlab command window:

Interior-point solution summary
  Problem status  : PRIMAL_INFEASIBLE
  Solution status : PRIMAL_INFEASIBLE_CER
  Dual.    obj: 3.0499696430e-01    nrm: 3e-01    Viol.  con: 0e+00    var: 4e-11    cones: 0e+00  
Optimizer summary
  Optimizer                 -                        time: 0.20    
    Interior-point          - iterations : 23        time: 0.17    
      Basis identification  -                        time: 0.00    
        Primal              - iterations : 0         time: 0.00    
        Dual                - iterations : 0         time: 0.00    
        Clean primal        - iterations : 0         time: 0.00    
        Clean dual          - iterations : 0         time: 0.00    
    Simplex                 -                        time: 0.00    
      Primal simplex        - iterations : 0         time: 0.00    
      Dual simplex          - iterations : 0         time: 0.00    
    Mixed integer           - relaxations: 0         time: 0.00    


Hmm, something went wrong!


ans =


Unbounded objective function (MOSEK)

Could you please have a look at them? I would highly appreciate your response.

Regards, 

Wei

[Johan Löfberg]

As you already noticed, the model is unbounded, so what is the actual question?

https://yalmip.github.io/debuggingunbounded/