Hi,
Is there any way to have the limited-memory, gradient-based minimizers
call an external routine that provides an exact line-search result?
I am trying to find the minima of functions that have huge numbers of
variables, but which are structurally quite simple (incommensurate
phase-field crystal models). The limited memory algorithms I've tried
either converge to very poor solutions, or never terminate. I suspect
that this may have to do with continuous symmetries that make the
Hessian semidefinite, though I've tried constraining the obvious ones.
I was hoping that exact line-searches might help escape regions that may
be shallow but not flat. The form of the energy functional reduces a
line-search to minimizing a quartic polynomial that is not too hard to
compute, which may make the extra effort worthwhile.
Best,
Rodrigo
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