Search directions in the SDP and the monotone SDLCP: generalization and inexact computation

We propose a family of directions that generalizes many directions proposed so far in feasible-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.