[petsc-users] Does PETSc have these solvers bounded-constrained optimization problems?

[Justin Chang]

Attached is my petsc4py/firedrake code which has the implementation I
described.

As of right now, my current implementation with ASILS/ASFLS solvers work
(although they are much slower compared to TRON) but the SSILS/SSFLS
solvers don't even converge.

For example, if I run the code as:

> python NR_Nonlinear_poisson.py 50 50 2 -opt_tao_type asils
-opt_tao_monitor -opt_tao_max_it 10 -opt_tao_view
iter =   0, Function value: 10.268,  Residual: 30.1512
iter =   1, Function value: 2.26616,  Residual: 3.28276
iter =   2, Function value: 0.442395,  Residual: 0.409106
iter =   3, Function value: 0.0180227,  Residual: 0.0305439
iter =   4, Function value: 0.00381325,  Residual: 0.0134287
iter =   5, Function value: 0.00191598,  Residual: 0.00599256
iter =   6, Function value: 0.00114725,  Residual: 0.00383069
iter =   7, Function value: 0.000888807,  Residual: 0.0032619
iter =   8, Function value: 0.000434005,  Residual: 0.00148022
iter =   9, Function value: 0.000179781,  Residual: 0.000565633
iter =  10, Function value: 7.54948e-05,  Residual: 0.000242123
iter =  11, Function value: 3.14898e-05,  Residual: 0.000112043
Tao Object:(opt_) 1 MPI processes
  type: asils
  TaoLineSearch Object:  (opt_)   1 MPI processes
    type: armijo
  KSP Object:  (opt_)   1 MPI processes
    type: gmres
  total KSP iterations: 511
  Active Set subset type: subvec
  convergence tolerances: gatol=1e-16,   steptol=0.,   gttol=0.
  Residual in Function/Gradient:=0.000112043
  convergence tolerances: function minimum=1e-08
  Objective value=3.14898e-05
  total number of iterations=11,                          (max: 10)
  total number of constraint function evaluations=23
  total number of Jacobian evaluations=12
  Solver terminated: -2   Maximum Iterations

The above indicates that the solver converges. However if I run the same
code but with this:

> python NR_Nonlinear_poisson.py 50 50 2 -opt_tao_type ssils
-opt_tao_monitor -opt_tao_max_it 10 -opt_tao_view
iter =   0, Function value: 10.268,  Residual: 30.1512
iter =   1, Function value: 10.268,  Residual: 30.1512
iter =   2, Function value: 10.268,  Residual: 30.1512
iter =   3, Function value: 10.268,  Residual: 30.1512
iter =   4, Function value: 10.268,  Residual: 30.1512
iter =   5, Function value: 10.268,  Residual: 30.1512
iter =   6, Function value: 10.268,  Residual: 30.1512
iter =   7, Function value: 10.268,  Residual: 30.1512
iter =   8, Function value: 10.268,  Residual: 30.1512
iter =   9, Function value: 10.268,  Residual: 30.1512
iter =  10, Function value: 10.268,  Residual: 30.1512
iter =  11, Function value: 10.268,  Residual: 30.1512
Tao Object:(opt_) 1 MPI processes
  type: ssils
  TaoLineSearch Object:  (opt_)   1 MPI processes
    type: armijo
  KSP Object:  (opt_)   1 MPI processes
    type: gmres
  total KSP iterations: 451
  Active Set subset type: subvec
  convergence tolerances: gatol=1e-16,   steptol=0.,   gttol=0.
  Residual in Function/Gradient:=30.1512
  convergence tolerances: function minimum=1e-08
  Objective value=10.268
  total number of iterations=11,                          (max: 10)
  total number of constraint function evaluations=331
  total number of Jacobian evaluations=1
  Solver terminated: -2   Maximum Iterations

Clearly something is wrong. Any insight as to why?

Thanks,
Justin

On Tue, Jun 14, 2016 at 6:29 AM, Jed Brown <jed at jedbrown.org> wrote:

> Barry Smith <bsmith at mcs.anl.gov> writes:
> >    In Tao it is solving it as an optimization problem while
> >    SNESVINEWTONSSLS solves it as a "nonlinear equation" with
> >    constraints; I think the answer should be the same.
>
> The latter may have more solutions.
>
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