Unknown status in solving QP( quadratic programming)

[wang lingyi]

Hi,

I am trying to solve a quadratic programming (QP) problem using mosek within matlab 2018a and yalmip. My problem has equality and inequality constraints. The debug data file and solver output are attached as below. The problem is that the solver status is "unknown" and the  dual constraint violations  taken from the command "check(F)"  is shown to be negative (dual infeasible). My question is:

1、Why the problem is dual infeasible?

2、What does the "unknown" status implies?

3、how can I deal with this problem? 

Thank you very much for any useful advice~

[Erling D. Andersen]

You using version 9.3.6. I would recommend upgrading to latest version 9.3.20.

1. 

The problem

min x

is dual infeasible because the dual problem problem has no solution.

I cannot say why your problem is dual infeasible. Maybe you forgot some important constraints or the objective function is wrong.

I can recommend to study

https://docs.mosek.com/modeling-cookbook/duality.html

2. 

MOSEK chooses to dualize the problem It somehow makes your problem hard so if you force it to solve the primal it solves nicely.

See

https://docs.mosek.com/latest/toolbox/solver-parameters.html

https://docs.mosek.com/latest/toolbox/parameters.html#mosek.iparam.intpnt_solve_form

for info about how to do that.

3. Your problem is badly scaled

Frequency of nonzero matrix coeficients
           Interval   #            Rel.(%)
    [10^-12,10^-11[:  15           1.44
    [10^-11,10^-10[:  5            0.48
      [10^-8,10^-7[:  4            0.38
      [10^-7,10^-6[:  5            0.48
      [10^-5,10^-4[:  135          12.92
      [10^-4,10^-3[:  29           2.78
      [10^-3,10^-2[:  43           4.11
      [10^-2,10^-1[:  98           9.38
       [10^-1,10^0[:  699          66.89
        [10^0,10^1[:  12           1.15
                All:  1045

The smallest element in A in absolute size should >=1.0e-6 I would recommend.