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.