Existence of Search Directions in Interior-Point Algorithms for the SDP and the Monotone SDLCP

Masayuki Shida, Susumu Shindoh and Masakazu Kojima

Various search directions used in interior-point-algorithms for the SDP (semidefinite program) and the monotone SDLCP (semidefinite linear complementarity problem) are characterized by the intersection of a maximal monotone affine subspace and a maximal and strictly antitone affine subspace. This observation provides a unified geometric view over the existence of those search directions.

Research Report B-310, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro, Tokyo 152 Japan, January 1996.

Contact: kojima@is.titech.ac.jp