[petsc-users] Tao iterations

[Jed Brown]

Justin Chang <jychang48 at gmail.com> writes:

> Hi Jason,
>
> One more question about BLMVM... if it only uses gradient information and
> does not require the definitition of a Hessian Matrix, can this method be
> applied to solve problems that are nonsymmetric by nature? (e.g.,
> advection-diffusion equations). 

Such equations do not have an associated objective functional, thus you
don't have the "gradient" of something, you just have a system of
nonlinear equations.  (There are ways to formulate such systems as
optimization, but they have issues like you mention.)  Reformulating
nonlinear equations as optimization can also turn a problem with a
unique solution into one with local minima, for which it may be
impossible to guarantee that you have reached a global minimum.

Use SNES for solving nonlinear equations.  You can try the quasi-Newton
methods, which are related to BLMVM.
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