Questions about solvebilevel.

[MK]

Dear sir, 

        When i run my model with the solvebilevle, it ends with the output that "Infeasible in solver".

        However, the inner and outer problem are all linear program. 

        Any suggestions? I have attached the files below. Any help will be greatly appreciated.

     

[Johan Löfberg]

you're not telling us which solvers you are using

[MK]

Sorry for that.

Here is the output information.

* Starting YALMIP bilevel solver.

* Outer solver   : QUADPROG

* Inner solver   : QUADPROG

* Max iterations : 300

 Node       Upper       Gap(%)      Lower    Open

    1 :          Inf      Inf            Inf   0  Infeasible in solver

[MK]

I didn't change the default solver.

[Johan Löfberg]

YALMIP picks the best possible, which in your case is quadprog (which isn't that good...)

However, the problem you have is that the outer problem is nonconvex. THe local solver quadprog fails miserably. It doesn't even manage to solve the problem with inner optimality removed

optimize([server_cons(price),user_cons(a)],server_obj(a,price),sdpsettings('solver','quadprog'))

  struct with fields:

    yalmipversion: '20181012'

       yalmiptime: 0.3186

       solvertime: 0.2754

             info: 'Infeasible problem (QUADPROG)'

          problem: 1

That problem is trivially feasible though

optimize([server_cons(price),user_cons(a)])

    yalmipversion: '20181012'

       yalmiptime: 0.3259

       solvertime: 0.0791

             info: 'Successfully solved (GUROBI-GUROBI)'

          problem: 0

However, trying to solve a bilvel problem with nonconvex outer problem is optimistic, to say the least...but your problem appears to be trivial as bmibnb easily solves it to global optimality

[res1,res2]=solvebilevel(server_cons(price),server_obj(a,price),user_cons(a),user_obj(a,price),a,sdpsettings('bilevel.outersolver','bmibnb'))

* Starting YALMIP bilevel solver.

* Outer solver   : BMIBNB

* Inner solver   : GUROBI-GUROBI

* Max iterations : Inf

 Node       Upper       Gap(%)      Lower    Open

    1 :    0.000E+00     0.00      0.000E+00   0  Solved to optimality

res1 = 

  struct with fields:

    problem: 0

res2 = 

  struct with fields:

          upper: 0

           iter: 1

    ninfeascuts: 0

       ndomcuts: 0