Search Directions in the SDP and the Monotone SDLCP: Generalization and Inexact Computation

Masakazu Kojima, Masayuki Shida and Susumu Shindoh

We propose a family of directions that generalizes many directions proposed so far in interior-point methods for the SDP (semidefinite programming) and for the monotone SDLCP (semidefinite linear complementarity problem). We derive the family from the Helmberg-Rendl-Vanderbei-Wolkowicz/Kojima-Shindoh-Hara/Monteiro direction by relaxing its ``centrality equation'' into a ``centrality inequality.'' Using this family, we present a predictor-corrector infeasible-interior-point method to provide a theoretical basis for inexact computation of directions in primal-dual interior-point methods for the SDP.

Research Report B-327, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 157, Japan, March 1997.