Infeasibility certificates for systems of inequalities

[Thomas Kahle]

Hi,

I'm trying to use yalmip (and mosek if that matters) to investigate the (in)feasibility of polynomial inequality systems.  I'm not yet interested in optimization. One way I (ab)use yalmip for this task is for instance the following simple code:

l1 = sdpvar (1,1); l2=sdpvar(1,1); l3=sdpvar(1,1);
h = -l1;
F = [l1*l2 + l2*l3 + l3*l1 >= 4,
 l1 <= 1, l1 >= 0,
 l2 <= 1, l2 >= 0,
 l3 <= 1, l3 >= 0]
solvemoment(F,h,[],2);

This yields

  Problem status  : DUAL_INFEASIBLE
  Solution status : DUAL_INFEASIBLE_CER

What are ways to investigate the infeasibility certificate from yalmip?  Are there any?

In general, if I'm only interested in feasibility of inequality systems. What are good ways to investigate this with yalmip?

[Johan Löfberg]

There are no dedicated ways to study infeasibility.

[Johan Löfberg]

and I wouldn't call this abuse. Infeasibility of polynomials problems is hard, and studying the feasibility of the SDP relaation is a reasonable way to detect infeasibility in a guaranteed way

[Erling D. Andersen]

Note the status tells you that the dual problem is infeasible. So saying the problem is infeasible is wrong if you mean the primal infeasibilite.

Hence your problem is unbounded given it has a feasible solution.

[Johan Löfberg]

The moment solver done some primal-dual switch, so the important flag is the yalmip diagnostics, which says infeasible

    yalmiptime: 0.0611

    solvertime: 0.2409

          info: 'Infeasible problem (MOSEK)'

       problem: 1