Solution should be f(1,1)=-2 
  0 TAO,  Function value: 8.,  Residual: 24496.1 
  0 TAO,  Function value: -5.43278,  Residual: 955.461 
  1 TAO,  Function value: -1.91991,  Residual: 203.127 
  2 TAO,  Function value: -1.89878,  Residual: 2.30255 
  3 TAO,  Function value: -1.95114,  Residual: 0.143794 
  4 TAO,  Function value: -1.99671,  Residual: 0.0248563 
  5 TAO,  Function value: -1.99999,  Residual: 0.00206264 
  6 TAO,  Function value: -2.,  Residual: 7.6949e-06 
Tao Object: 1 MPI processes
  type: ipm
  KSP Object: 1 MPI processes
    type: preonly
    maximum iterations=10000, initial guess is zero
    tolerances:  relative=1e-05, absolute=1e-50, divergence=10000.
    left preconditioning
    using NONE norm type for convergence test
  PC Object: 1 MPI processes
    type: lu
      out-of-place factorization
      tolerance for zero pivot 2.22045e-14
      matrix ordering: nd
      factor fill ratio given 0., needed 0.
        Factored matrix follows:
          Mat Object: 1 MPI processes
            type: superlu
            rows=15, cols=15
            package used to perform factorization: superlu
            total: nonzeros=0, allocated nonzeros=0
            total number of mallocs used during MatSetValues calls=0
              SuperLU run parameters:
                Equil: NO
                ColPerm: 3
                IterRefine: 0
                SymmetricMode: NO
                DiagPivotThresh: 1.
                PivotGrowth: NO
                ConditionNumber: NO
                RowPerm: 0
                ReplaceTinyPivot: NO
                PrintStat: NO
                lwork: 0
    linear system matrix = precond matrix:
    Mat Object: 1 MPI processes
      type: seqaij
      rows=15, cols=15
      total: nonzeros=40, allocated nonzeros=48
      total number of mallocs used during MatSetValues calls=0
        not using I-node routines
  total KSP iterations: 14
  Active Set subset type: subvec
  convergence tolerances: gatol=1e-05,   steptol=0.,   gttol=0.
  Residual in Function/Gradient:=7.6949e-06
  Objective value=-2.
  total number of iterations=7,                          (max: 200)
  total number of function/gradient evaluations=8,      (max: 500)
  total number of Hessian evaluations=8
  total number of constraint function evaluations=16
  Solution converged:    ||g(X)|| <= gatol
