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

[Justin Chang]

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)
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?

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.

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
> >
> >
> >
>
>
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