On search directions in interior-point methods for semidefinite programming
We discuss several different search directions which can be used in
primal-dual interior-point methods for semidefinite programming problems
and investigate their theoretical properties, including scale
invariance, primal-dual symmetry, and whether they always generate
well-defined directions. Among the directions satisfying all but
at most two of these desirable properties are the Alizadeh-Haeberly-Overton,
Nesterov-Todd, Gu, and Toh directions, as well as directions we will call
the MTW and Half directions. The first five of these appear to be the best
in our limited computational testing also.
Technical Report No. 1205, School of Operations Research and
Cornell University, Ithaca, NY 14853-3801.