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

[Barry Smith]

> On Jun 13, 2016, at 5:25 PM, Justin Chang <jychang48 at gmail.com> wrote:
> 
> Thanks Barry,
> 
> 1) Say this is my problem:
> 
> min 1/2 x^T*H*x - x^T*f
> s.t. x_lower < x < x_upper
> 
> If i want to use any of the following TAO complementarity solvers:
> 
> - ASILS
> - ASFLS
> - SSILS
> - SSFLS
> 
> I would need these routines:
> 
> TaoSetConstraintsRoutine(tao,c,formGradient(...),NULL)

   I think this should be TaoSetGradientRoutine()

> TaoSetJacobianRoutine(tao,J,J,formHessian(...),NULL)
> TaoSetVariableBounds(tao,x_lower,x_upper)
> 
> where formGradient() would return c = H*x - f
> and formHessian would return J = H
> 
> Is this correct?

  Seems reasonable.

> 
> 2) If so, then what exactly is the difference between these TAO complementarity solvers and the SNESVINEWTONSSLS solver? From the online manuals and documentation, both claim to be variational inequality solvers.

   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.

  Barry

> 
> Thanks!
> Justin
>  
> 
> On Sat, Jun 11, 2016 at 12:19 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> 
>    Justin,
> 
> For bound constrained optimization problems, there is:
> 
>  TRON -- a truncated Newton method from your favorite inventor of such methods
>  BLMVM -- a limited memory quasi-Newton method for bound constraints (projected quasi-Newton)
> 
> There used to be the KT solvers that was just a wrapper around the complementarity
> methods.  Jason -- what happened to this?
> 
> Anyways, from the gradient and Hessian (or Hessian vector product), you can apply the
> complementarity solvers to the optimality conditions:
> 
>  ASLS -- active set family (e.g. projected newton)
>  SSLS -- semismooth family
> 
> For more general constraints, there is:
> 
>  IPM -- interior-point method
> 
> I have not used it or tested it though.
> 
> For PDE constrained problems, there is:
> 
>  LCL -- linearly constrained augmented Lagrangian.
> 
> 
> ROL has imitations either directly copied from our code or written from our papers.
> 
> > On Jun 10, 2016, at 5:57 PM, Justin Chang <jychang48 at gmail.com> wrote:
> >
> > Hi all,
> >
> > Does PETSc currently have any of these solvers for bounded constraint problems:
> >
> > 1) Semismooth Newton methods (aka primal-dual active-set methods)
> > 2) Projected Newton methods
> >
> > Trilinos' Rapid Optimization Library (ROL) has them, and I have seen papers and books claiming that these solvers are state-of-the-art.
> >
> > I see there's SNESVINEWTONSSLS and TAOGPCG but are these the same as the above methods?
> >
> > Thanks,
> > Justin
> >
> >
> >
> 
>