pde constrained optimization with NonlinearSolver() ?

Question

Is it possible to deal with pde constrained optimization problems using
SNES solver and the goal function minimization last parameter
of NonlinearSolver?

Something like an pde solver with non-negative bound constrains
and a goal function?

( the documentation of NonlinearSolver goal function minimization is
sparse... )

Answer 1

It is possible to deal with constraint optimization problem. Look at the following:

http://fenicsproject.org/documentation/dolfin/1.4.0/cpp/programmers-reference/nls/PETScSNESSolver.html

You set solver parameters and then define the nonlinear variational form of the problem along with appropriate lower and upper bounds in the function space that you are solving the problem. Finally, few lines can solve your problem (Assuming a_min and a_max are lower and upper bounds of the solution:

solver  = NonlinearVariationalSolver(problem)
solver.parameters.update(snes_solver_parameters)
a_min = Function(interpolate(Constant(0.0), S))
a_max = Function(interpolate(Constant(1.0), S))
(iter, converged) = solver.solve(a_min.vector(), a_max.vector())

Comments

Navid, I ask a new question with just a few modifications
on demo_contact-vi-snes.py in order to obtain
bound non linear PDE constrained optimization with FEniCS:

http://fenicsproject.org/qa/5670/function-minization-constrains-adaptativenonlinearsolver

Any help will be apreciate.

Thank you very much for your time.

Andre Machado