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Minimize in LAMMPS means 0K. I don't know what it means
to minimize at a finite T, at least for MD.
To relax at a high T does not mean minimize, but to run dynamics
at a high T and let the system equlibrate. E.g. run a few 1000 steps
with fix nvt or some other thermostat.
To anneal, just means to change the temperature at some desired
rate. The various thermostats can all ramp their target T over the
course of a long run, by specifying an initial and final T. So you
can do an anneal that way.