
---- Minimum Surface Area Problem -----
mx:4, my:4
  0 TAO,  Function value: 0.210375,  Residual: 0.403597
  1 TAO,  Function value: 0.0110611,  Residual: 0.0197949
  2 TAO,  Function value: 4.46353e-05,  Residual: 8.72583e-05
  3 TAO,  Function value: 8.12611e-10,  Residual: 1.80227e-09
Tao Object: 1 MPI process
  type: ssils
  TaoLineSearch Object: 1 MPI process
    type: armijo
      Armijo linesearch    : alpha=1. beta=0.5     sigma=0.0001     memsize=1
    maximum function evaluations=30
    tolerances: ftol=0.0001, rtol=1e-10, gtol=0.9
    total number of function evaluations=1
    total number of gradient evaluations=1
    total number of function/gradient evaluations=0
    Termination reason: SUCCESS
  KSP Object: 1 MPI process
    type: gmres
      restart=30, using classical (unmodified) Gram-Schmidt orthogonalization with no iterative refinement
      happy breakdown tolerance=1e-30
    maximum iterations=10000, initial guess is zero
    tolerances: relative=1e-05, absolute=1e-50, divergence=10000.
    left preconditioning
    using PRECONDITIONED norm type for convergence test
  PC Object: 1 MPI process
    type: ilu
      out-of-place factorization
      0 levels of fill
      tolerance for zero pivot 2.22045e-14
      matrix ordering: natural
      factor fill ratio given 1., needed 1.
        Factored matrix:
          Mat Object: 1 MPI process
            type: seqaij
            rows=16, cols=16
            package used to perform factorization: petsc
            total: nonzeros=82, allocated nonzeros=82
              not using I-node routines
    linear system matrix, which is also used to construct the preconditioner:
    Mat Object: 1 MPI process
      type: seqaij
      rows=16, cols=16
      total: nonzeros=82, allocated nonzeros=112
      total number of mallocs used during MatSetValues calls=0
        not using I-node routines
  total KSP iterations: 13
  Active Set subset type: subvec
  convergence tolerances: gatol=1e-16,   grtol=0., steptol=0.,   gttol=1e-05
  Residual in Function/Gradient:=1.80227e-09
  convergence tolerances: catol=1e-08,   crtol=1e-08
  Residual in Constraints:=0.
  convergence tolerances: function minimum=1e-08
  Objective value=8.12611e-10
  total number of iterations=3,                          (max: 2000)
  total number of constraint function evaluations=7
  total number of Jacobian evaluations=4
  Solution converged:    Minf --  f < fmin
